Chapter 7Resource Masters
Consumable Workbooks Many of the worksheets contained in the Chapter ResourceMasters are available as consumable workbooks in both English and Spanish.
ISBN10 ISBN13
Study Guide and Intervention Workbook 0-07-877344-X 978-0-07-877344-0
Skills Practice Workbook 0-07-877346-6 978-0-07-877346-4
Practice Workbook 0-07-877347-4 978-0-07-877347-1
Word Problem Practice Workbook 0-07-877349-0 978-0-07-877349-5
Spanish Versions
Study Guide and Intervention Workbook 0-07-877345-8 978-0-07-877345-7
Practice Workbook 0-07-877348-2 978-0-07-877348-8
Answers for Workbooks The answers for Chapter 7 of these workbooks can be found in the back of this Chapter Resource Masters booklet.
StudentWorks PlusTM This CD-ROM includes the entire Student Edition test along withthe English workbooks listed above.
TeacherWorks PlusTM All of the materials found in this booklet are included for viewing,printing, and editing in this CD-ROM.
Spanish Assessment Masters (ISBN10: 0-07-877350-4, ISBN13: 978-0-07-877350-1)These masters contain a Spanish version of Chapter 7 Test Form 2A and Form 2C.
Copyright © by the McGraw-Hill Companies, Inc. All rights reserved. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with Glencoe Geometry. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.
Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240
ISBN13: 978-0-07-873964-4ISBN10: 0-07-873964-0 Geometry CRM7
Printed in the United States of America
1 2 3 4 5 6 7 8 9 10 009 13 12 11 10 09 08 07 06
CONTENTS
Teacher’s Guide to Using the Chapter 7Resource Masters . . . . . . . . . . . . . . . . . . . . iv
Chapter ResourcesStudent-Built Glossary . . . . . . . . . . . . . . . . . . . 1Anticipation Guide (English) . . . . . . . . . . . . . . . 3Anticipation Guide (Spanish) . . . . . . . . . . . . . . 4
Lesson 7-1ProportionsLesson Reading Guide. . . . . . . . . . . . . . . . . . . 5Study Guide and Intervention . . . . . . . . . . . . . . 6Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . . 8Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Word Problem Practice . . . . . . . . . . . . . . . . . 10Enrichment. . . . . . . . . . . . . . . . . . . . . . . . . . . 11Graphing Calculator . . . . . . . . . . . . . . . . . . . . 12
Lesson 7-2Similar PolygonsLesson Reading Guide. . . . . . . . . . . . . . . . . . 13Study Guide and Intervention . . . . . . . . . . . . . 14Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 16Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Word Problem Practice . . . . . . . . . . . . . . . . . 18Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Lesson 7-3Similar TrianglesLesson Reading Guide. . . . . . . . . . . . . . . . . . 20Study Guide and Intervention . . . . . . . . . . . . . 21Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 23Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Word Problem Practice . . . . . . . . . . . . . . . . . 25Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Lesson 7-4Parallel Lines and Proportional PartsLesson Reading Guide. . . . . . . . . . . . . . . . . . 27Study Guide and Intervention . . . . . . . . . . . . . 28Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 30Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Word Problem Practice . . . . . . . . . . . . . . . . . 32Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Lesson 7-5Parts of Similar TrianglesLesson Reading Guide. . . . . . . . . . . . . . . . . . 34Study Guide and Intervention . . . . . . . . . . . . . 35Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 37Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38Word Problem Practice . . . . . . . . . . . . . . . . . 39Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 40Spreadsheet . . . . . . . . . . . . . . . . . . . . . . . . . 41
AssessmentStudent Recording Sheet . . . . . . . . . . . . . . . . 43Rubric for Pre-AP. . . . . . . . . . . . . . . . . . . . . . 44Chapter 7 Quizzes 1 and 2. . . . . . . . . . . . . . . 45Chapter 7 Quizzes 3 and 4. . . . . . . . . . . . . . . 46Chapter 7 Mid-Chapter Test . . . . . . . . . . . . . . 47Chapter 7 Vocabulary Test . . . . . . . . . . . . . . . 48Chapter 7 Test, Form 1 . . . . . . . . . . . . . . . . . 49Chapter 7 Test, Form 2A . . . . . . . . . . . . . . . . 51Chapter 7 Test, Form 2B . . . . . . . . . . . . . . . . 53Chapter 7 Test, Form 2C . . . . . . . . . . . . . . . . 55Chapter 7 Test, Form 2D . . . . . . . . . . . . . . . . 57Chapter 7 Test, Form 3 . . . . . . . . . . . . . . . . . 59Chapter 7 Extended-Response Test . . . . . . . . 61Standardized Test Practice. . . . . . . . . . . . . . . 62
Answers . . . . . . . . . . . . . . . . . . . . . . .A1–A29
iii
Teacher’s Guide to Using theChapter 7 Resource Masters
The Chapter 7 Resource Masters includes the core materials needed for Chapter 7.These materials include worksheets, extensions, and assessment options. Theanswers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing onthe TeacherWorks PlusTM CD-ROM.
Chapter ResourcesStudent-Built Glossary (pages 1–2)These masters are a student study tool that presents up to twenty of the keyvocabulary terms from the chapter.Students are to recording definitions and/orexamples for each term. You may suggestthat student highlight or star the termswith which they are not familiar. Give tostudents before beginning Lesson 7-1.Encourage them to add these pages to theirmathematics study notebooks. Remindthem to complete the appropriate words asthey study each lesson.
Anticipation Guide (pages 7–8) Thismaster presented in both English andSpanish is a survey used before beginningthe chapter to pinpoint what students mayor may not know about the concepts in thechapter. Students will revisit this surveyafter they complete the chapter to see iftheir perceptions have changed.
Lesson ResourcesLesson Reading Guide Get Ready for theLesson reiterates the questions from thebeginning of the Student Edition lesson.Read the Lesson asks students to interpretthe context of and relationships amongterms in the lesson. Finally, RememberWhat You Learned asks students tosummarize what they have learned usingvarious representation techniques. Use as astudy tool for note taking or as an informalreading assignment. It is also a helpful toolfor ELL (English Language Learners).
Study Guide and Intervention Thesemasters provide vocabulary, key concepts,additional worked-out examples and Check Your Progress exercises to use as areteaching activity. It can also be used inconjunction with the Student Edition as aninstructional tool for students who havebeen absent.
Skills Practice This master focuses moreon the computational nature of the lesson.Use as an additional practice option or ashomework for second-day teaching of thelesson.
Practice This master closely follows thetypes of problems found in the Exercisessection of the Student Edition and includesword problems. Use as an additionalpractice option or as homework for second-day teaching of the lesson.
Word Problem Practice This masterincludes additional practice in solving wordproblems that apply the concepts of thelesson. Use as an additional practice or ashomework for second-day teaching of thelesson.
Enrichment These activities may extendthe concepts of the lesson, offer a historicalor multicultural look at the concepts,or widen students’ perspectives on themathematics they are learning. They arewritten for use with all levels of students.
iv
Graphing Calculator, ScientificCalculator, or Spreadsheet ActivitiesThese activities present ways in whichtechnology can be used with the concepts in some lessons of this chapter. Use as analternative approach to some concepts or as an integral part of your lessonpresentation.
Assessment OptionsThe assessment masters in the Chapter 7Resource Masters offer a wide range ofassessment tools for formative (monitoring)assessment and summative (final)assessment.
Student Recording Sheet This mastercorresponds with the standardized testpractice at the end of the chapter.
Pre-AP Rubric This master providesinformation for teachers and students onhow to assess performance on open-endedquestions.
Quizzes Four free-response quizzes offerassessment at appropriate intervals in thechapter.
Mid-Chapter Test This 1-page testprovides an option to assess the first half ofthe chapter. It parallels the timing of theMid-Chapter Quiz in the Student Editionand includes both multiple-choice and free-response questions.
Vocabulary Test This test is suitable forall students. It includes a list of vocabularywords and 10 questions to assess students’knowledge of those words. This can also beused in conjunction with one of the leveledchapter tests.
Leveled Chapter Tests• Form 1 contains multiple-choice
questions and is intended for use withbelow grade level students.
• Forms 2A and 2B contain multiple-choice questions aimed at on grade levelstudents. These tests are similar informat to offer comparable testingsituations.
• Forms 2C and 2D contain free-responsequestions aimed at on grade levelstudents. These tests are similar informat to offer comparable testingsituations.
• Form 3 is a free-response test for usewith above grade level students.
All of the above mentioned tests include afree-response Bonus question.
Extended-Response Test Performanceassessment tasks are suitable for allstudents. Sample answers and a scoringrubric are included for evaluation.
Standardized Test Practice These threepages are cumulative in nature. It includesthree parts: multiple-choice questions withbubble-in answer format, griddablequestions with answer grids, and short-answer free-response questions.
Answers• The answers for the Anticipation Guide
and Lesson Resources are provided asreduced pages with answers appearing in red.
• Full-size answer keys are provided forthe assessment masters.
v
Chapter 7 1 Glencoe Geometry
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Student-Built GlossaryNAME ______________________________________________ DATE ____________ PERIOD _____
7
Ch
apte
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esThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 7.As you study the chapter, complete each term’s definition or description. Rememberto add the page number where you found the term. Add these pages to yourGeometry Study Notebook to review vocabulary at the end of the chapter.
Vocabulary Term Found on Page Definition/Description/Example
cross products
extremes
means
midsegment
(continued on the next page)
Chapter 7 2 Glencoe Geometry
Student-Built Glossary (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
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Vocabulary Term Found on Page Definition/Description/Example
proportion
ratio
scale factor
similar polygons
Chapter 7 3 Glencoe Geometry
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Anticipation GuideProportions and Similarity
NAME ______________________________________________ DATE ____________ PERIOD _____
7
Before you begin Chapter 7
• Read each statement.
• Decide whether you Agree (A) or Disagree (D) with the statement.
• Write A or D in the first column OR if you are not sure whether you agree ordisagree, write NS (Not Sure).
After you complete Chapter 7
• Reread each statement and complete the last column by entering an A or a D.
• Did any of your opinions about the statements change from the first column?
• For those statements that you mark with a D, use a piece of paper to write anexample of why you disagree.
STEP 1
STEP 2
STEP 1 Statement STEP 2A, D, or NS A or D
1. Ratios are always written as fractions.
2. A proportion is an equation stating that two ratios are equal.
3. Two ratios are in proportion to each other only if their cross products are equal.
4. If �ab� � �d
c�, then �
ac� � �
db�.
5. The ratio of the lengths of the sides of similar figures is called the scale factor for the two figures.
6. If one angle in a triangle is congruent to an angle in another triangle, then the two triangles are similar.
7. If a line is parallel to one side of a triangle and intersects the other two sides in two distinct points, then the line separates the two sides into congruent segments.
8. A segment whose endpoints are the midpoints of two sides of a triangle is parallel to the third side of the triangle.
9. If two triangles are similar then their perimeters are equal.
10. The medians of two similar triangles are in the same proportion as corresponding sides.
Ch
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Capítulo 7 4 Geometría de Glencoe
Ejercicios preparatoriosProporciones y semejanzas
NOMBRE ____________________________________________ FECHA ____________ PERÍODO _____
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Antes de comenzar el Capítulo 7
• Lee cada enunciado.
• Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado.
• Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta,escribe NS (No estoy seguro(a).
Después de completar el Capítulo 7
• Vuelve a leer cada enunciado y completa la última columna con una A o una D.
• ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna?
• En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con losenunciados que marcaste con una D.
PASO 1
PASO 2
PASO 1 Enunciado PASO 2A, D o NS A o D
1. Las razones se escriben siempre como fracciones.
2. Una proporción es una ecuación que establece que dos razones son iguales.
3. Dos razones son proporcionales entre sí sólo si sus productos cruzados son iguales.
4. Si �ab� � �d
c�, entonces �
ac� � �
db�.
5. La razón de las longitudes de los lados de figuras semejantes se llama factor de escala para las dos figuras.
6. Si un ángulo de un triángulo es congruente a un ángulo de otro triángulo, entonces los dos triángulos son semejantes.
7. Si una recta es paralela a un lado del triángulo e interseca los otros dos lados en dos puntos diferentes, entonces la recta separa los dos lados en segmentos congruentes.
8. Un segmento cuyos extremos son los puntos medios de dos lados de un triángulo es paralelo al tercer lado del triángulo.
9. Si dos triángulos son semejantes, éstos tienen el mismo perímetro.
10. Las medianas de dos triángulos semejantes están en la misma proporción que los lados correspondientes.
Chapter 7 5 Glencoe Geometry
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Lesson Reading GuideProportions
NAME ______________________________________________ DATE ____________ PERIOD _____
7-1
Get Ready for the LessonRead the introduction to Lesson 7-1 in your textbook.
Estimate the ratio of length to width for the background rectangles in Tiffany’sClematis Skylight.
Read the Lesson
1. Match each description in the first column with a word or phrase from the secondcolumn.
a. The ratio of two corresponding quantities i. proportion
b. r and u in the equation �rs� � �u
t� ii. cross products
c. a comparison of two quantities iii. means
d. ru and st in the equation �rs� � �u
t� iv. scale factor
e. an equation stating that two ratios are equal v. extremes
f. s and t in the equation �rs� � �u
t� vi. ratio
2. If m, n, p, and q are nonzero numbers such that �mn� � �
pq�, which of the following
statements could be false?
A. np � mq B. �np
� � �mq�
C. mp � nq D. qm � pn
E. �mn� � �p
q� F. �p
q� � �m
n�
G. m:p � n:q H. m:n � p:q
3. Write two proportions that match each description.
a. Means are 5 and 8; extremes are 4 and 10.
b. Means are 5 and 4; extremes are positive integers that are different from means.
Remember What You Learned
4. Sometimes it is easier to remember a mathematical idea if you put it into words withoutusing any mathematical symbols. How can you use this approach to remember theconcept of equality of cross products?
Less
on
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Chapter 7 6 Glencoe Geometry
Study Guide and InterventionProportions
NAME ______________________________________________ DATE ____________ PERIOD _____
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Write Ratios A ratio is a comparison of two quantities. The ratio a to b, where b is not zero, can be written as �
ab� or a:b. The ratio of two quantities is sometimes called a scale
factor. For a scale factor, the units for each quantity are the same.
In 2002, the Chicago Cubs baseball team won 67 games out of 162.Write a ratio for the number of games won to the total number of games played.To find the ratio, divide the number of games won by the total number of games played. The
result is �16672�, which is about 0.41. The Chicago Cubs won about 41% of their games in 2002.
A doll house that is 15 inches tall is a scale model of a real housewith a height of 20 feet. What is the ratio of the height of the doll house to theheight of the real house?To start, convert the height of the real house to inches.20 feet � 12 inches per foot � 240 inchesTo find the ratio or scale factor of the heights, divide the height of the doll house by theheight of the real house. The ratio is 15 inches:240 inches or 1:16. The height of the doll
house is �116� the height of the real house.
1. In the 2005 Major League baseball season, Alex Rodriquez hit 48 home runs and was at bat 605 times. Find the ratio of home runs to the number of times he was at bat.
2. There are 182 girls in the sophomore class of 305 students. Find the ratio of girls to total students.
3. The length of a rectangle is 8 inches and its width is 5 inches. Find the ratio of length to width.
4. The sides of a triangle are 3 inches, 4 inches, and 5 inches. Find the scale factor betweenthe longest and the shortest sides.
5. The length of a model train is 18 inches. It is a scale model of a train that is 48 feet long.Find the scale factor.
Example 1
Example 2
Exercises
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Chapter 7 7 Glencoe Geometry
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Study Guide and Intervention (continued)
Proportions
NAME ______________________________________________ DATE ____________ PERIOD _____
7-1
Use Properties of Proportions A statement that two ratios are equal is called aproportion. In the proportion �
ab� � �d
c�, where b and d are not zero, the values a and d are
the extremes and the values b and c are the means. In a proportion, the product of themeans is equal to the product of the extremes, so ad � bc.
�ab� � �d
c�
a � d � b � c↑ ↑
extremes means
Solve �196� � �
2x7�.
�196� � �
2x7�
9 � x � 16 � 27 Cross products
9x � 432 Multiply.
x � 48 Divide each side by 9.
A room is 49 centimeters by 28 centimeters on a scale drawing of a house. For the actual room, the larger dimension is 14 feet.Find the shorter dimension of the actual room.If x is the room’s shorter dimension, then
�2489� � �1
x4�
49x � 392 Cross products
x � 8 Divide each side by 49.
The shorter side of the room is 8 feet.
Solve each proportion.
1. �12� � �
2x8� 2. �
38� � �2
y4� 3. �
xx
��
222
� � �3100�
4. �183.2� � �
9y� 5. �
2x8� 3� � �
54� 6. �
xx
��
11� � �
34�
Use a proportion to solve each problem.
7. If 3 cassettes cost $44.85, find the cost of one cassette.
8. The ratio of the sides of a triangle are 8:15:17. If the perimeter of the triangle is 480 inches, find the length of each side of the triangle.
9. The scale on a map indicates that one inch equals 4 miles. If two towns are 3.5 inchesapart on the map, what is the actual distance between the towns?
shorter dimension���longer dimension
Example 1
Example 2
Exercises
Less
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Chapter 7 8 Glencoe Geometry
Skills PracticeProportions
NAME ______________________________________________ DATE ____________ PERIOD _____
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1. FOOTBALL A tight end scored 6 touchdowns in 14 games. Find the ratio of touchdownsper game.
2. EDUCATION In a schedule of 6 classes, Marta has 2 elective classes. What is the ratioof elective to non-elective classes in Marta’s schedule?
3. BIOLOGY Out of 274 listed species of birds in the United States, 78 species made theendangered list. Find the ratio of endangered species of birds to listed species in theUnited States.
4. ART An artist in Portland, Oregon, makes bronze sculptures of dogs. The ratio of theheight of a sculpture to the actual height of the dog is 2:3. If the height of the sculptureis 14 inches, find the height of the dog.
5. SCHOOL The ratio of male students to female students in the drama club at CampbellHigh School is 3:4. If the number of male students in the club is 18, what is the numberof female students?
Solve each proportion.
6. �25� � �4
x0� 7. �1
70� � �
2x1� 8. �
250� � �
46x�
9. �54x� � �
385� 10. �
x �3
1� � �
72� 11. �
135� � �
x �5
3�
Find the measures of the sides of each triangle.
12. The ratio of the measures of the sides of a triangle is 3:5:7, and its perimeter is 450 centimeters.
13. The ratio of the measures of the sides of a triangle is 5:6:9, and its perimeter is 220 meters.
14. The ratio of the measures of the sides of a triangle is 4:6:8, and its perimeter is 126 feet.
15. The ratio of the measures of the sides of a triangle is 5:7:8, and its perimeter is 40 inches.
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Chapter 7 9 Glencoe Geometry
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PracticeProportions
NAME ______________________________________________ DATE ____________ PERIOD _____
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1. NUTRITION One ounce of cheddar cheese contains 9 grams of fat. Six of the grams of fatare saturated fats. Find the ratio of saturated fats to total fat in an ounce of cheese.
2. FARMING The ratio of goats to sheep at a university research farm is 4:7.The number of sheep at the farm is 28. What is the number of goats?
3. ART Edward Hopper’s oil on canvas painting Nighthawks has a length of 60 inches and a width of 30 inches. A print of the original has a length of 2.5 inches. What is the width of the print?
Solve each proportion.
4. �58� � �1
x2� 5. �1.
x12� � �
15� 6. �2
67x� � �
43�
7. �x �
32
� � �89� 8. �
3x4� 5� � �
�75� 9. �
x �4
2� � �
x �2
4�
Find the measures of the sides of each triangle.
10. The ratio of the measures of the sides of a triangle is 3:4:6, and its perimeter is 104 feet.
11. The ratio of the measures of the sides of a triangle is 7:9:12, and its perimeter is 84 inches.
12. The ratio of the measures of the sides of a triangle is 6:7:9, and its perimeter is 77 centimeters.
Find the measures of the angles in each triangle.
13. The ratio of the measures of the angles is 4:5:6.
14. The ratio of the measures of the angles is 5:7:8.
15. BRIDGES The span of the Benjamin Franklin suspension bridge in Philadelphia,Pennsylvania, is 1750 feet. A model of the bridge has a span of 42 inches. What is theratio of the span of the model to the span of the actual Benjamin Franklin Bridge?
Less
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1. MODELS Luke wants to make a scalemodel of a Boeing 747 jetliner. He wantsevery foot of his model to represent 50feet. Complete the following table.
(Source: www.boeing.com)
2. RATIONS Sixteen students went on a week-long hiking trip. They broughtwith them 320 specially baked, protein-rich, cookies. What is the ratio of cookiesto students?
3. PHOTOGRAPHS Tracy is 4 feet tall and her father is 6 feet tall. In a photograph of the two of themstanding side by side, Tracy’s image is 2 inches tall.
Although their images are much smaller,the ratio of their heights remains thesame. How tall is Tracy’s father’s imagein the photo?
4. CARS A car company builds twoversions of one of its models—a sedanand a station wagon. The ratio of sedansto station wagons is 11 : 2. A freighterbegins unloading the cars at a dock.Tom counts 18 station wagons and thenoverhears a dock worker call out, “Okay,that’s all of the wagons . . . bring out the sedans!” How many sedans were onthe ship?
MAPS For Exercises 5–7, use thefollowing information.Carlos makes a map of his neighborhood for a presentation. The scale of his map is 1 inch : 125 feet.
5. How many feet do 4 inches represent onthe map?
6. Carlos lives 250 feet away from Andrew.How many inches separate Carlos’ homefrom Andrew’s on the map?
7. During a practice run in front of hisparents, Carlos realizes that his map is far too small. He decides to make his map 5 times as large. What would be the scale of the larger map?
6 ft4 ft
Chapter 7 10 Glencoe Geometry
Word Problem PracticeProportions
NAME ______________________________________________ DATE ____________ PERIOD _____
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Actual ModelPart length (in.) length (in.)
Wing Span 2,537
Length 2,782
Tail Height 392 7.84
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Chapter 7 11 Glencoe Geometry
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EnrichmentNAME ______________________________________________ DATE ____________ PERIOD _____
7-1
Growth ChartsIt is said that when a child has reached the age of 2 years, he is roughly half of hisadult height. The growth chart below shows the growth according to percentiles forboys.
1. Use the chart to determine the approximate height for a boy at age 2 if he is inthe 75th to 95th percentile.
2. Using the rule that the height at age 2 is approximately half of his adult height,set up a proportion to solve for the adult height of the boy in exercise 1. Solveyour proportion.
3. Use the chart to approximate the height at age 18 for a boy if he is in the 75thto 95th percentile. How does this answer compare to the answer to problem 1?
4. Repeat this process for a boy who is in the 5th to 25th percentile.
5. Is using the rule that a boy is half of his adult height at age 2 years a goodapproximation? Explain.
85
75
65
55
45
35
2 4 6 8 10 12 14 16 18
Age (yr)
Hei
gh
t (i
n.)
Percentile Group
5th to 25th
25th to 75th
75th to 95th
A
B Less
on
7-1
05-42 Geo-07-873964 4/12/06 8:44 PM Page 11
Chapter 7 12 Glencoe Geometry
Graphing Calculator ActivitySolving Proportions
NAME ______________________________________________ DATE ____________ PERIOD _____
7-1C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
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-Hill C
ompanies, Inc.
You can use a calculator to solve proportions.
Solve the proportion by using cross products.
�5156..69
� � �45
x.8�
Multiply 16.9 by 45.8. Divide the product by 55.6.
Enter: 16.9 45.8 55.6 13.92122302
The solution is approximately 13.921.
Solve each proportion by using cross products. Round your answers to the nearest hundredth.
1. �1339..98
� � �10
x.5� 2. �
2357..97
� � �24
x.3� 3. �
1594..63
� � �27
x.7�
4. �6463..84
� � �16
x.9� 5. �
7357..42
� � �32
x.4� 6. �
46x.2� � �
2396..74
�
7. �14
x.9� � �
1264..86
� 8. �35
x.8� � �
3227..98
� 9. �46
x.9� � �
1959..79
�
10. �3241..91
� � �36
x.6� 11. �
99x.8� � �
3425..23� 12. �
68x.9� � �
4846..34
�
ENTER��
Example
05-42 Geo-07-873964 4/12/06 8:44 PM Page 12
Chapter 7 13 Glencoe Geometry
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Lesson Reading GuideSimilar Polygons
NAME ______________________________________________ DATE ____________ PERIOD _____
7-2
Get Ready for the LessonRead the introduction to Lesson 7-2 in your textbook.• Describe the figures that have similar shapes.
• What happens to the figures as your eyes move from the center to the outer edge?
Read the Lesson1. Complete each sentence.
a. Two polygons that have exactly the same shape, but not necessarily the same size,are .
b. Two polygons are congruent if they have exactly the same shape and the same .
c. Two polygons are similar if their corresponding angles are and their corresponding sides are .
d. Two polygons are congruent if their corresponding angles are and their corresponding sides are .
e. The ratio of the lengths of corresponding sides of two similar figures is called the .
f. Multiplying the coordinates of all points of a figure in the coordinate plane by a scale factor to get a similar figure is called a .
g. If two polygons are similar with a scale factor of 1, then the polygons are .
2. Determine whether each statement is always, sometimes, or never true.a. Two similar triangles are congruent.b. Two equilateral triangles are congruent.c. An equilateral triangle is similar to a scalene triangle.d. Two rectangles are similar.e. Two isosceles right triangles are congruent.f. Two isosceles right triangles are similar.g. A square is similar to an equilateral triangle.h. Two acute triangles are similar.i. Two rectangles in which the length is twice the width are similar.j. Two congruent polygons are similar.
Remember What You Learned3. A good way to remember a new mathematical vocabulary term is to relate it to words
used in everyday life. The word scale has many meanings in English. Give three phrasesthat include the word scale in a way that is related to proportions.
Less
on
7-2
05-42 Geo-07-873964 4/12/06 8:44 PM Page 13
Chapter 7 14 Glencoe Geometry
Study Guide and InterventionSimilar Polygons
NAME ______________________________________________ DATE ____________ PERIOD _____
7-2C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
Identify Similar Figures
Determine whether the triangles are similar.Two polygons are similar if and only if their corresponding angles are congruent and their corresponding sides are proportional.
�C � �Z because they are right angles, and �B � �X.By the Third Angle Theorem, �A � �Y.
For the sides, �BX
CZ� � �
2203�, �
BX
AY� � � �
2203�, and �
AY
CZ� � �
2203�.
The side lengths are proportional. So �BCA � �XZY.
Is polygon WXYZ � polygon PQRS?
For the sides, �WPQ
X� � �
182� � �
32�, �Q
XYR� � �
1182� � �
32�, �R
YZS� � �
1150� � �
32�,
and �ZSWP� � �
96� � �
32�. So corresponding sides are proportional.
Also, �W � �P, �X � �Q, �Y � �R, and �Z � �S, so corresponding angles are congruent. We can conclude that polygon WXYZ � polygon PQRS.
Determine whether each pair of figures is similar. If they are similar, give theratio of corresponding sides.
1. 2.
3. 4. 10y
8y
37�
37�116�
27�
5x
4x
15z12z
22
11
1610
equilateral triangles
15
9
12
18
XW
Z Y10
6
8
12
QP
S R
20�2��23�2�
20 23
2320 20��2 23��245�
45�C A X Z
B YExample 1
Example 2
Exercises
05-42 Geo-07-873964 4/12/06 8:44 PM Page 14
Chapter 7 15 Glencoe Geometry
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Study Guide and Intervention (continued)
Similar Polygons
NAME ______________________________________________ DATE ____________ PERIOD _____
7-2
Scale Factors When two polygons are similar, the ratio of the lengths of corresponding sides is called the scale factor. At the right, �ABC � �XYZ. The scale factor of �ABC to �XYZ is 2 and the scale factor of
�XYZ to �ABC is �12�.
3 cm
6 cm
8 cm
10 cm5 cm4 cm
Z
Y
XC
A
B
The two polygons aresimilar. Find x and y.
Use the congruent angles to write thecorresponding vertices in order.�RST � �MNPWrite proportions to find x and y.
�3126� � �1
x3� �
3y8� � �
3126�
16x � 32(13) 32y � 38(16)x � 26 y � 19
x
y38
3216 13
T
S
R P
N
M
�ABC � �CDE. Find the scale factor and find the lengths of C�D�and D�E�.
AC � 3 � 0 � 3 and CE � 9 � 3 � 6. Thescale factor of �CDE to �ABC is 6:3 or 2:1.Using the Distance Formula,AB � �1 � 9� � �10� and BC � �4 � 9� � �13�. The lengths of thesides of �CDE are twice those of �ABC,so DC � 2(BA) or 2�10� and DE � 2(BC) or 2�13�.
x
y
A(0, 0)
B(1, 3)
C(3, 0)
E(9, 0)
D
Each pair of polygons is similar. Find x and y.
1. 2.
3. 4.
5. In Example 2 above, point D has coordinates (5, 6). Use the Distance Formula to verifythe lengths of C�D� and D�E�.
40
36x
30
18 y12
y � 1
18
24
x18
10
y
4.5x
2.5
5
9
12
y8
10x
Example 1 Example 2
Exercises
Less
on
7-2
05-42 Geo-07-873964 4/12/06 8:44 PM Page 15
Chapter 7 16 Glencoe Geometry
Skills PracticeSimilar Polygons
NAME ______________________________________________ DATE ____________ PERIOD _____
7-2C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
Determine whether each pair of figures is similar. Justify your answer.
1. 2.
Each pair of polygons is similar. Write a similarity statement, and find x, themeasure(s) of the indicated side(s), and the scale factor.
3. G�H� 4. S�T� and S�U�
5. W�T� 6. T�S� and S�P�
10
8
x � 2
x � 1
SP
M N
L
T
9
103
x � 1
5
P
S
RU V
WT
Q
x � 5
x � 5
9
3
44 S
W
XY
T
U26
14
12 13
B C
DA
13
76 x
G
E H
F
7.5
7.5
7.57.5
Z Y
XW
3
3
33S R
QP
10.5
6 9
59� 35�A C
B
7
4 659� 35�D F
E
05-42 Geo-07-873964 4/12/06 8:44 PM Page 16
Chapter 7 17 Glencoe Geometry
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PracticeSimilar Polygons
NAME ______________________________________________ DATE ____________ PERIOD _____
7-2
Determine whether each pair of figures is similar. Justify your answer.
1. 2.
Each pair of polygons is similar. Write a similarity statement, and find x, themeasure(s) of the indicated side(s), and the scale factor.
3. L�M� and M�N� 4. D�E� and D�F�
5. COORDINATE GEOMETRY Triangle ABC has vertices A(0, 0), B(�4, 0), and C(�2, 4).The coordinates of each vertex are multiplied by 3 to create �AEF. Show that �AEF issimilar to �ABC.
6. INTERIOR DESIGN Graham used the scale drawing of his living room to decide where to place furniture. Find the dimensions of theliving room if the scale in the drawing is 1 inch � 4.5 feet.
4 in.
21–2 in.
6 12
40�
40�
x � 1
x � 3AF
E
D
B C14
10
x � 6
x � 9
C N MD
A B LP
2412
14 162118
VUAC
B T
25 12
9
14.4
1524
20
15
JM Q R
SP
KL
Less
on
7-2
05-42 Geo-07-873964 4/12/06 8:44 PM Page 17
Chapter 7 18 Glencoe Geometry
Word Problem PracticeSimilar Polygons
NAME ______________________________________________ DATE ____________ PERIOD _____
7-2C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
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-Hill C
ompanies, Inc.
1. PANELS When closed, an entertainmentcenter is made of four square panels.The three smaller panels are congruentsquares.
What is the scale factor of the largersquare to one of the smaller squares?
2. DOWNSPOUTS During a storm, one of the downspouts on Mr. Herrera’shouse was broken and needed to bereplaced. Unfortunately, the downspoutwas too damaged to measure its lengthand it was too difficult to measure theheight of the gutter. Luckily, Mr. Herrerahad a scale model of his house. If the downspout in the model was 1�
12� feet
long and the scale factor was 20, howlong was the actual downspout?
3. ORIGAMI Baxter uses an 8-inch square piece of origami paper to makean origami model of a chicken. Whenfinished, the chicken stands 4 incheshigh. Baxter wants to make anotherorigami chicken, only this time he wants to make it 12 inches high instead.What size piece of paper should he useto do this?
4. ENLARGING Camille wants to make a pattern for a four-pointed star withdimensions twice as long as the oneshown. Help her by drawing a star withdimensions twice as long on the gridbelow.
BIOLOGY For Exercises 5–7, use thefollowing information.A paramecium is a small single-cellorganism. The paramecium magnified belowis actually one tenth of a millimeter long.
5. If you want to make a photograph of theoriginal paramecium so that its image is1 centimeter long, by what scale factorshould you magnify it?
6. If you want to make a photograph of theoriginal paramecium so that its image is15 centimeters long, by what scale factorshould you magnify it?
7. By approximately what scale factor hasthe paramecium been enlarged to makethe image shown?
05-42 Geo-07-873964 4/12/06 8:44 PM Page 18
Chapter 7 19 Glencoe Geometry
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EnrichmentNAME ______________________________________________ DATE ____________ PERIOD _____
7-2
Constructing Similar PolygonsHere are four steps for constructing a polygon that is similar to and with sides twice as long as those of an existing polygon.
Step 1 Choose any point either inside or outside the polygon and label it O.Step 2 Draw rays from O through each vertex of the polygon.Step 3 For vertex V, set the compass to length OV. Then locate a new point
V� on ray OV such that VV� � OV. Thus, OV� � 2(OV ).Step 4 Repeat Step 3 for each vertex. Connect points V�, W�, X� and Y� to
form the new polygon.
Two constructions of polygons similar to and with sides twice those of VWXYare shown below. Notice that the placement of point O does not affect the sizeor shape of V�W�X�Y�, only its location.
Trace each polygon. Then construct a similar polygon with sides twice as long asthose of the given polygon.
1. 2. D E F
GC
A
B
VW
Y X
VW
Y X
V�
W�
X�Y�
O
VW
YX
V�
W�
X�Y�
O
3. Explain how to construct a similarpolygon with sides three times the lengthof those of polygon HIJKL. Then do theconstruction.
4. Explain how to construct a similar
polygon 1�12� times the length of those of
polygon MNPQRS. Then do theconstruction.
M
S
R
N
Q
P
H I
LK
J
Less
on
7-2
05-42 Geo-07-873964 4/12/06 8:44 PM Page 19
Chapter 7 20 Glencoe Geometry
Lesson Reading GuideSimilar Triangles
NAME ______________________________________________ DATE ____________ PERIOD _____
7-3C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
Get Ready for the LessonRead the introduction to Lesson 7-3 in your textbook.• What does it mean to say that triangular shapes result in rigid construction?
• What would happen if the shapes used in the construction were quadrilaterals?
Read the Lesson1. State whether each condition guarantees that two triangles are congruent or similar.
If the condition guarantees that the triangles are both similar and congruent, writecongruent. If there is not enough information to guarantee that the triangles will becongruent or similar, write neither.a. Two sides and the included angle of one triangle are congruent to two sides and the
included angle of the other triangle.b. The measures of all three pairs of corresponding sides are proportional.c. Two angles of one triangle are congruent to two angles of the other triangle.d. Two angles and a nonincluded side of one triangle are congruent to two angles and
the corresponding nonincluded side of the other triangle.e. The measures of two sides of a triangle are proportional to the measures of two
corresponding sides of another triangle, and the included angles are congruent.
f. The three sides of one triangle are congruent to the three sides of the other triangle.
g. The three angles of one triangle are congruent to the three angles of the other triangle.
h. One acute angle of a right triangle is congruent to one acute angle of another righttriangle.
i. The measures of two sides of a triangle are proportional to the measures of two sidesof another triangle.
2. Identify each of the following as an example of a reflexive, symmetric, or transitive property.a. If �RST � �UVW, then �UVW � �RST.b. If �RST � �UVW and �UVW � �OPQ, then �RST � �OPQ.c. �RST � �RST
Remember What You Learned3. A good way to remember something is to explain it to someone else. Suppose one of your
classmates is having trouble understanding the difference between SAS for congruenttriangles and SAS for similar triangles. How can you explain the difference to him?
05-42 Geo-07-873964 4/12/06 8:44 PM Page 20
Chapter 7 21 Glencoe Geometry
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Study Guide and InterventionSimilar Triangles
NAME ______________________________________________ DATE ____________ PERIOD _____
7-3
Identify Similar Triangles Here are three ways to show that two triangles are similar.
AA Similarity Two angles of one triangle are congruent to two angles of another triangle.
SSS Similarity The measures of the corresponding sides of two triangles are proportional.
SAS SimilarityThe measures of two sides of one triangle are proportional to the measures of two corresponding sides of another triangle, and the included angles are congruent.
Determine whether thetriangles are similar.
�DAC
F� � �69� � �
23�
�BE
CF� � �1
82� � �
23�
�DAB
E� � �1105� � �
23�
�ABC � �DEF by SSS Similarity.
15
129
D E
F
10
86
A B
C
Determine whether thetriangles are similar.
�34� � �
68�, so �MQR
N� � �
NRS
P�.
m�N � m�R, so �N � �R.�NMP � �RQS by SAS Similarity.
8
4
70�
Q
R S6
370�
M
N P
Determine whether each pair of triangles is similar. Justify your answer.
1. 2.
3. 4.
5. 6. 32
20
154025
24
3926
1624
18
8
65�9
465�
36
2018
24
Example 1 Example 2
Exercises
Less
on
7-3
05-42 Geo-07-873964 4/12/06 8:44 PM Page 21
Chapter 7 22 Glencoe Geometry
Study Guide and Intervention (continued)
Similar Triangles
NAME ______________________________________________ DATE ____________ PERIOD _____
7-3C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
Use Similar Triangles Similar triangles can be used to find measurements.
�ABC � �DEF.Find x and y.
�DAC
F� � �BE
CF� �D
ABE� � �
BE
CF�
� �198� �1
y8� � �
198�
18x � 9(18�3�) 9y � 324x � 9�3� y � 36
18�3��x
18��3
B
CA
18 18 9y
x
E
FD
A person 6 feet tall castsa 1.5-foot-long shadow at the same timethat a flagpole casts a 7-foot-longshadow. How tall is the flagpole?
The sun’s rays form similar triangles.Using x for the height of the pole, �
6x� � �
17.5�,
so 1.5x � 42 and x � 28.The flagpole is 28 feet tall.
7 ft
6 ft?
1.5 ft
Each pair of triangles is similar. Find x and y.
1. 2.
3. 4.
5. 6.
7. The heights of two vertical posts are 2 meters and 0.45 meter. When the shorter postcasts a shadow that is 0.85 meter long, what is the length of the longer post’s shadow to the nearest hundredth?
y
x32
10
2230yx
9
8
7.2
16
yx
6038.6
23
3024
36��2yx
3636
20
13
26y
x � 235
13
10 20y
x
Example 1 Example 2
Exercises
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Chapter 7 23 Glencoe Geometry
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Skills PracticeSimilar Triangles
NAME ______________________________________________ DATE ____________ PERIOD _____
7-3
Determine whether each pair of triangles is similar. Justify your answer.
1. 2.
3. 4.
ALGEBRA Identify the similar triangles, and find x and the measures of theindicated sides.
5. A�C� and E�D� 6. J�L� and L�M�
7. E�H� and E�F� 8. V�T� and S�T�
6
14
S
U
V
R T
x � 4
x � 612
9
6
9
D
E
FH
Gx � 5
16
4M
NL
J
K
x � 18
x � 3
1512
D
E CB
Ax � 1
x � 5
30�60�RQ
M
S
K
T
2170�
15
MJ
P
1470�10
U
S
T
12
128
9
9 6
C P
QR
A
B
2014
13 1221
9
S W X
Y
R
T
Less
on
7-3
05-42 Geo-07-873964 4/12/06 8:44 PM Page 23
Chapter 7 24 Glencoe Geometry
PracticeSimilar Triangles
NAME ______________________________________________ DATE ____________ PERIOD _____
7-3C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
Determine whether each pair of triangles is similar. Justify your answer.
1. 2.
ALGEBRA Identify the similar triangles, and find x and the measures of theindicated sides.
3. L�M� and Q�P� 4. N�L� and M�L�
Use the given information to find each measure.
5. If T�S� || Q�R�, TS � 6, PS � x � 7, 6. If E�F� || H�I�, EF � 3, EG � x � 1,QR � 8, and SR � x � 1, HI � 4, and HG � x � 3,find PS and PR. find EG and HG.
INDIRECT MEASUREMENT For Exercises 7 and 8, use the following information.A lighthouse casts a 128-foot shadow. A nearby lamppost that measures 5 feet 3 inches castsan 8-foot shadow.
7. Write a proportion that can be used to determine the height of the lighthouse.
8. What is the height of the lighthouse?
F
GE
H
I
S RP
QT
8
N
J LK
Mx � 5
6x � 2
24
12
18N
P
QL
M
x � 3x � 1
18
16 12.516
14
11
M
L N
S R
T42�
42�
24
1812
16J
A K
Y S
W
05-42 Geo-07-873964 4/12/06 8:44 PM Page 24
Chapter 7 25 Glencoe Geometry
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Word Problem PracticeSimilar Triangles
NAME ______________________________________________ DATE ____________ PERIOD _____
7-3
Less
on
7-3
1. MINIATURES Marla likes her chair so much that she decides to make aminiature replica of it for her pethamster. Find the value of x.
2. MODELS Jim has a scale model of hissailboat. The figure shows drawings ofthe original sailboat and the model.Find x.
3. GEOMETRY Georgia draws a regularpentagon and starts connecting itsvertices to make a 5-pointed star. Afterdrawing three of thelines in the star, shebecomes curiousabout two trianglesthat appear in thefigure, �ABC and�BCE. They look similar to her. Provethat this is the case.
4. SHADOWS A radio tower casts ashadow 8 feet long at the same time that a vertical yardstick casts a shadowhalf an inch long. How tall is the radiotower?
MOUNTAIN PEAKS For Exercises 5 and6, use the following information.Gavin and Brianna want to know how far amountain peak is from their houses. Theymeasure the angles between the line of siteto the peak and to each other’s houses andcarefully make the drawing shown.
The actual distance between Gavin and Brianna’s house is 1�
12� miles.
5. What is the actual distance of themountain peak from Gavin’s house?Round your answer to the nearest tenth of a mile.
6. What is the actual distance of themountain peak from Brianna’s house?Round your answer to the nearest tenth of a mile.
Gavin
Brianna
Peak
2 in.
2.015 in.0.246 in.
90˚83˚
A
B
D
E
C
52˚
203 in.
10.15 in. 8 in.52˚
x in.
14”
3.5”
15”
x
05-42 Geo-07-873964 4/12/06 8:44 PM Page 25
Chapter 7 26 Glencoe Geometry
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
7-3
Moving ShadowsHave you ever watched your shadow as you walked along the street at night and observedhow its shape changes as you move? Supposea man who is 6 feet tall is standing below a lamppost that is 20 feet tall. The man iswalking away from the lamppost at a rate of 5 feet per second.
1. If the man is moving at a rate of 5 feet persecond, make a conjecture as to the ratethat his shadow is moving.
2. How far away from the lamppost is the man after 8 seconds?
3. How far is the end of his shadow from the bottom of the lamppost after 8 seconds? Use similar triangles to solve this problem.
4. After 3 more seconds, how far from the lamppost is the man? How far from thelamppost is his shadow?
5. How many feet did the man move in 3 seconds? How many feet did the shadowmove in 3 seconds?
6. The man is moving at a rate of 5 feet/second. What rate is his shadow moving?How does this rate compare to the conjecture you made in problem 1? Make aconjecture as to why the results are like this.
20 ft
6 ft
x ft
5 ft/sec
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Chapter 7 27 Glencoe Geometry
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Lesson Reading GuideParallel Lines and Proportional Parts
NAME ______________________________________________ DATE ____________ PERIOD _____
7-4
Get Ready for the LessonRead the introduction to Lesson 7-4 in your textbook.
Use a geometric idea to explain why the distance between Chicago Avenue andOntario Street is shorter along Michigan Avenue than along Lake Shore Drive.
Read the Lesson
1. Provide the missing words to complete the statement of each theorem. Then state thename of the theorem.
a. If a line intersects two sides of a triangle and separates the sides into corresponding
segments of lengths, then the line is to the
third side.
b. A midsegment of a triangle is to one side of the triangle and its
length is the length of that side.
c. If a line is to one side of a triangle and intersects the other two sides
in distinct points, then it separates these sides into
of proportional length.
2. Refer to the figure at the right.
a. Name the three midsegments of �RST.
b. If RS � 8, RU � 3, and TW � 5, find the length of each of themidsegments.
c. What is the perimeter of �RST?
d. What is the perimeter of �UVW?
e. What are the perimeters of �RUV, �SVW, and �TUW?
f. How are the perimeters of each of the four small triangles related to the perimeter ofthe large triangle?
g. Would the relationship that you found in part f apply to any triangle in which themidpoints of the three sides are connected?
Remember What You Learned
3. A good way to remember a new mathematical term is to relate it to other mathematicalvocabulary that you already know. What is an easy way to remember the definition ofmidsegment using other geometric terms?
R
U
V
W
T
S
Less
on
7-4
05-42 Geo-07-873964 4/12/06 8:45 PM Page 27
Chapter 7 28 Glencoe Geometry
Study Guide and InterventionParallel Lines and Proportional Parts
NAME ______________________________________________ DATE ____________ PERIOD _____
7-4C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
Proportional Parts of Triangles In any triangle, a line parallel to one side of a triangle separates the other two sides proportionally. The converse is also true.
If X and Y are the midpoints of R�T� and S�T�, then X�Y� is amidsegment of the triangle. The Triangle Midsegment Theoremstates that a midsegment is parallel to the third side and is half its length.
If XY��� || RS���, then �RXTX� � �Y
SYT�.
If �RXTX� � �Y
SYT�, then XY��� || RS���.
If X�Y� is a midsegment, then XY��� || RS��� and XY � �12�RS.
Y ST
R
X
In �ABC, E�F� || C�B�. Find x.
Since E�F� || C�B�, �FA
BF� � �E
AEC�.
�xx
��
222
� � �168�
6x � 132 � 18x � 3696 � 12x8 � x
F
C
BA
18
x � 22 x � 2
6E
A triangle has verticesD(3, 6), E(�3, �2), and F(7, �2).Midsegment G�H� is parallel to E�F�. Find the length of G�H�.G�H� is a midsegment, so its length is one-half that of E�F�. Points E and F have thesame y-coordinate, so EF � 7 � (�3) � 10.The length of midsegment G�H� is 5.
Find x.
1. 2. 3.
4. 5. 6.
7. In Example 2, find the slope of E�F� and show that E�F� || G�H�.
30 10x � 10
x11x � 12
x33
30 10
24x
35
x9
20
x
185
5 x
7
Example 1 Example 2
Exercises
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Chapter 7 29 Glencoe Geometry
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Study Guide and Intervention (continued)
Parallel Lines and Proportional Parts
NAME ______________________________________________ DATE ____________ PERIOD _____
7-4
Divide Segments Proportionally When three or more parallel lines cut two transversals,they separate the transversals into proportional parts. If the ratio of the parts is 1, then the parallellines separate the transversals into congruent parts.
If �1 || �2 || �3, If �4 || �5 || �6 and
then �ab� � �d
c�. �
uv� � 1, then �
wx� � 1.
Refer to lines �1, �2 ,and �3 above. If a � 3, b � 8, and c � 5, find d.
�1 || �2 || �3 so �38� � �d
5�. Then 3d � 40 and d � 13�
13�.
Find x and y.
1. 2.
3. 4.
5. 6.16 32
y � 3y
3 4
x � 4x
5
8 y � 2
y2x � 4
3x � 1 2y � 2
3y
2x � 6
x � 3
12
x � 12 12
3x5x
a
bd
u v
xw
ctn
m
s �1
�4 �5 �6
�2
�3
Example
Exercises
Less
on
7-4
05-42 Geo-07-873964 4/12/06 8:45 PM Page 29
Chapter 7 30 Glencoe Geometry
Skills PracticeParallel Lines and Proportional Parts
NAME ______________________________________________ DATE ____________ PERIOD _____
7-4C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
1. If JK � 7, KH � 21, and JL � 6, 2. Find x and TV if RU � 8, US � 14,find LI. TV � x � 1 and VS � 17.5.
Determine whether B�C� || D�E�.
3. AD � 15, DB � 12, AE � 10, and EC � 8
4. BD � 9, BA � 27, and CE is one third of EA
5. AE � 30, AC � 45, and AD is twice DB
COORDINATE GEOMETRY For Exercises 6–8, use the following information.Triangle ABC has vertices A(�5, 2), B(1, 8), and C(4, 2). Point Dis the midpoint of A�B� and E is the midpoint of A�C�.
6. Identify the coordinates of D and E.
7. Show that B�C� is parallel to D�E�.
8. Show that DE � �12�BC.
9. Find x and y. 10. Find x and y.
3–2x � 2
x � 3
2y � 1
3y � 52x � 1 3y � 8
y � 5x � 7
x
y
O
A C
B
D
E
C
B
E
D
A
R
U V
T
S
HL
K J
I
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Chapter 7 31 Glencoe Geometry
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PracticeParallel Lines and Proportional Parts
NAME ______________________________________________ DATE ____________ PERIOD _____
7-4
1. If AD � 24, DB � 27, and EB � 18, 2. Find x, QT, and TR if QT � x � 6,find CE. SR � 12, PS � 27, and TR � x � 4.
Determine whether J�K� || N�M�.
3. JN � 18, JL � 30, KM � 21, and ML � 35
4. KM � 24, KL � 44, and NL � �56�JN
COORDINATE GEOMETRY For Exercises 5 and 6, use the following information.Triangle EFG has vertices E(�4, �1), F(2, 5), and G(2, �1). Point Kis the midpoint of E�G� and H is the midpoint of F�G�.
5. Show that E�F� is parallel to K�H�.
6. Show that KH � �12�EF.
7. Find x and y. 8. Find x and y.
9. MAPS The distance from Wilmington to Ash Grove along Kendall is 820 feet and along Magnolia, 660 feet. If the distance between Beech and Ash Grove along Magnolia is 280 feet, what is the distance between the two streets alongKendall?
Ash Grove
Beech
Magnolia Kendall
Wilmington
4–3y � 2
3x � 4 x � 1
4y � 43x � 4
2–3y � 3
1–3y � 65–
4x � 3
x
y
O
E G
F
H
K
N LJ
KM
S
Q
TRP
D
E
C
BA
Less
on
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Chapter 7 32 Glencoe Geometry
Word Problem PracticeParallel Lines and Proportional Parts
NAME ______________________________________________ DATE ____________ PERIOD _____
7-4C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
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-Hill C
ompanies, Inc.
1. CARPENTRY Jake isfixing an A-frame.He wants to add ahorizontal supportbeam halfway up and parallel to the ground. Howlong should thisbeam be?
2. STREETS In the diagram, Cay Streetand Bay Street are parallel. Find x.
3. JUNGLE GYMS Prassad is building atwo-story jungle gym according to theplans shown. Find x.
4. FIREMEN A cat is stuck in a treeand firemen try torescue it. Basedon the figure, if afireman climbs to the top of theladder, how faraway is the cat?
EQUAL PARTS For Exercises 5 and 6,use the following information.Nick has a stick that he would like to divide into 9 equal parts. He places it on a piece of grid paper as shown. The grid paper is ruled so that vertical andhorizontal lines are equally spaced.
5. Explain how he can use the grid paperto help him find where he needs to cutthe stick.
6. Suppose Nick wants to divide his stickinto 5 equal parts utilizing the gridpaper. What can he do?
Meeeeowww!
30 ft.
40 ft.46 ft.
x
8 ft. 8 ft.
10 ft.
24 ft
.
10 ft.x
Cay St.
1 km 1.4 km
0.8 km
Bay St.
Dale
St. Earl St.
(not drawn to scale)
x
8 feet
05-42 Geo-07-873964 4/12/06 8:45 PM Page 32
Chapter 7 33 Glencoe Geometry
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EnrichmentNAME ______________________________________________ DATE ____________ PERIOD _____
7-4
Parallel Lines and Congruent PartsThere is a theorem stating that if three parallel lines cut off congruent segments on onetransversal, then they cut off congruent segments on any transversal. This can be shown forany number of parallel lines. The following drafting technique uses this fact to divide asegment into congruent parts.
A�B� is to be separated into five congruent parts. This can be done very accurately without using a ruler. All that is needed is a compass and a piece of notebook paper.
Step 1 Hold the corner of a piece of notebook paper at point A.
Step 2 From point A, draw a segment along the paper that is five spaces long. Mark where the lines of the notebook paper meet the segment. Label the fifth point, P.
Step 3 Draw P�B�. Through each of the other marks on A�P�, construct a line parallel to B�P�. The points where these lines intersect A�B� will divide A�B� into five congruent segments.
Use a compass and a piece of notebook paper to divide each segment into the given number of congruent parts.
1. six congruent parts
2. seven congruent parts A B
A B
A
P
B
A B
P
A B
A B
Less
on
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05-42 Geo-07-873964 4/12/06 8:45 PM Page 33
Chapter 7 34 Glencoe Geometry
Lesson Reading GuideParts of Similar Triangles
NAME ______________________________________________ DATE ____________ PERIOD _____
7-5C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
Get Ready for the LessonRead the introduction to Lesson 7-5 in your textbook.
• How is similarity involved in the process of making a photographic print from anegative?
• Why do photographers place their cameras on tripods?
Read the Lesson
1. In the figure, �RST � �UVW. Complete each proportion involving the lengths of segments inthis figure by replacing the question mark. Thenidentify the definition or theorem from the listbelow that the completed proportion illustrates.
i. Definition of congruent polygons ii. Definition of similar polygons
iii. Proportional Perimeters Theorem iv. Angle Bisectors Theorem
v. Similar triangles have corresponding altitudes proportional to corresponding sides.
vi. Similar triangles have corresponding medians proportional to corresponding sides.
vii. Similar triangles have corresponding angle bisectors proportional to corresponding sides.
a. �RS � S?T � TR� � �U
RSV� b. �U
RWT� � �
S?X�
c. �RU
MN� � �V
?W� d. �U
RSV� � �
S?T�
e. �RPS
P� � �S
?T� f. �
U?N� � �
UR
WT�
g. �WTP
Q� � �R?T� h. �
UVW
W� � �Q
?V�
Remember What You Learned
2. A good way to remember a large amount of information is to remember key words. Whatkey words will help you remember the features of similar triangles that are proportionalto the lengths of the corresponding sides?
W
Q N
YU
V
T
P M
XR
S
05-42 Geo-07-873964 4/12/06 8:45 PM Page 34
Chapter 7 35 Glencoe Geometry
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Study Guide and InterventionParts of Similar Triangles
NAME ______________________________________________ DATE ____________ PERIOD _____
7-5
Perimeters If two triangles are similar, their perimeters have the same proportion as the corresponding sides.
If �ABC � �RST, then
�AR
BS
��
BST
C��
RA
TC
� � �AR
BS� � �
BST
C� � �R
ACT�.
Use the diagram above with �ABC � �RST. If AB � 24 and RS � 15,find the ratio of their perimeters.Since �ABC � �RST, the ratio of the perimeters of �ABC and �RST is the same as theratio of corresponding sides.
Therefore � �2145�
� �85�
Each pair of triangles is similar. Find the perimeter of the indicated triangle.
1. �XYZ 2. �BDE
3. �ABC 4. �XYZ
5. �ABC 6. �RST
25
20
10
P T
SM
R
95
13
12
A D
E
C
B
5 6
8.7
13
10
X Y
Z T
R S18
20
25 15 17
8
NB
A C PM
36
9
11C
DE
A
B
44
24
20 22 10
TRX Z
YS
perimeter of �ABC���perimeter of �RST
A C
BS
R T
Example
Exercises
Less
on
7-5
05-42 Geo-07-873964 4/12/06 8:45 PM Page 35
Chapter 7 36 Glencoe Geometry
Study Guide and Intervention (continued)
Parts of Similar Triangles
NAME ______________________________________________ DATE ____________ PERIOD _____
7-5C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
Special Segments of Similar Triangles When two triangles are similar,corresponding altitudes, angle bisectors, and medians are proportional to the correspondingsides. Also, in any triangle an angle bisector separates the opposite side into segments thathave the same ratio as the other two sides of the triangle.
In the figure,�ABC � �XYZ, with angle bisectors asshown. Find x.
Since �ABC � �XYZ, the measures of theangle bisectors are proportional to themeasures of a pair of corresponding sides.
�AX
BY� � �Y
BWD�
�2x4� � �
180�
10x � 24(8)10x � 192
x � 19.2
2410
DW
Y
ZXC
B
A
8x
S�U� bisects �RST. Find x.
Since S�U� is an angle bisector, �RTU
U� � �
RTS
S�.
�2x0� � �
1350�
30x � 20(15)30x � 300
x � 10
x 20
3015
UT
S
R
Find x for each pair of similar triangles.
1. 2.
3. 4.
5. 6. 2x � 2x � 1
281617
11
x � 7
x
10
10x
8
873
3
4x
69
12x
x
36
1820
Example 1 Example 2
Exercises
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Chapter 7 37 Glencoe Geometry
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Skills PracticeParts of Similar Triangles
NAME ______________________________________________ DATE ____________ PERIOD _____
7-5
Find the perimeter of the given triangle.
1. �JKL, if �JKL � �RST, RS � 14, 2. �DEF, if �DEF � �ABC, AB � 27,ST � 12, TR � 10, and LJ � 14 BC � 16, CA � 25, and FD � 15
3. �PQR, if �PQR � �LMN, LM � 16, 4. �KLM, if �KLM � �FGH, FG � 30,MN � 14, NL � 27, and RP � 18 GH � 38, HF � 38, and KL � 24
Use the given information to find each measure.
5. Find FG if �RST � �EFG, S�H� is an 6. Find MN if �ABC � �MNP, A�D� is an altitude of �RST, F�J� is an altitude of altitude of �ABC, M�Q� is an altitude of�EFG, ST � 6, SH � 5, and FJ � 7. �MNP, AB � 24, AD � 14, and MQ � 10.5.
Find x.
7. �HKL � �XYZ 8.
LH
K
18
10
Y
15
x
ZX7
20
24
x
C
A
BD P NQ
M
JGE
F
HTR
S
GL
K
M
F
H
L MP Q
RN
A
B
C
D
E
F
R S
T
J K
L
Less
on
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05-42 Geo-07-873964 4/12/06 8:45 PM Page 37
Chapter 7 38 Glencoe Geometry
PracticeParts of Similar Triangles
NAME ______________________________________________ DATE ____________ PERIOD _____
7-5C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
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-Hill C
ompanies, Inc.
Find the perimeter of the given triangle.
1. �DEF, if �ABC � �DEF, AB � 36, 2. �STU, if �STU � �KLM, KL � 12,BC � 20, CA � 40, and DE � 35 LM � 31, MK � 32, and US � 28
Use the given information to find each measure.
3. Find PR if �JKL � �NPR, K�M� is an 4. Find ZY if �STU � �XYZ, U�A� is an altitude of �JKL, P�T� is an altitude of altitude of �STU, Z�B� is an altitude of �NPR, KL � 28, KM � 18, and �XYZ, UT � 8.5, UA � 6, and PT � 15.75. ZB � 11.4.
Find x.
5. 6.
PHOTOGRAPHY For Exercises 7 and 8, use the following information.Francine has a camera in which the distance from the lens to the film is 24 millimeters.
7. If Francine takes a full-length photograph of her friend from a distance of 3 meters andthe height of her friend is 140 centimeters, what will be the height of the image on thefilm? (Hint: Convert to the same unit of measure.)
8. Suppose the height of the image on the film of her friend is 15 millimeters. If Francinetook a full-length shot, what was the distance between the camera and her friend?
x28
20 30402x � 1 25x � 4
YX B
Z
TS A
U
MJ L
K
TN R
P
KS
LT
UMBE
CFD
A
05-42 Geo-07-873964 4/12/06 8:45 PM Page 38
Chapter 7 39 Glencoe Geometry
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Word Problem PracticeParts of Similar Triangles
NAME ______________________________________________ DATE ____________ PERIOD _____
7-5
Less
on
7-5
1. JOGGING Macy wants to jog aroundTriangle Park. On a scale map, the parkhas a perimeter of 11 inches. The scaleof the map is 1 inch : 100 yards. What isthe perimeter of the actual park?
2. TENTS Jana went camping and stayedin a tent shaped like a triangle. In aphoto of the tent, the base of the tent is6 inches and the altitude is 5 inches. Theactual base was 12 feet long. What wasthe height of the actual tent?
3. PLAYGROUND The playground atHank’s school has a large right trianglepainted in the ground. Hank starts at the right angle corner and walkstoward the opposite side along an anglebisector and stops when he gets to thehypotenuse.
How much farther from Hank is point Bversus point A?
4. FLAG POLES A flag pole attached tothe side of a building is supported with a network of strings as shown in thefigure.
The rigging is done so that AE � EF,AC � CD, and AB � BC. What is theratio of CF to BE?
COPIES For Exercises 5 and 6, use thefollowing information.Gordon made a photocopy of a page from his geometry book to enlarge one of thefigures. The actual figure that he copied isshown below.
The photocopy came out poorly. Gordoncould not read the numbers on thephotocopy, although the triangle itself was clear. Gordon measured the base of the enlarged triangle and found it to be 200 millimeters.
5. What is the length of the drawn altitudeof the enlarged triangle? Round youranswer to the nearest millimeter.
6. What is the length of the drawn medianof the enlarged triangle? Round youranswer to the nearest millimeter.
39 mm
Med
ian
Altit
ude
30 mm
29 mm
A BC
DF
E
A
B
45˚
30 ft
40 ft
50 ft
x
05-42 Geo-07-873964 4/12/06 8:45 PM Page 39
Another Proof of Pythagorean Theorem
1. For right triangle ABC with right angle C, and altitude C�D� as shown at the right, name three similar triangles.
2. List the three similar triangles as headings in the table below. Use the figure to complete thetable to list the corresponding parts of the threesimilar right triangles.
3. Use the corresponding parts of these similar triangles and their proportions to complete the statements in the proof and algebraically prove the Pythagorean Theorem.
Statements Reasons
1. Right triangle ABC with 1. Givenaltitute C�D�.
2. 2. Corresponding parts of similartriangles are in the same ratio
3. 3. Cross Products
4. 4. Addition Property of Equality
5. 5. Substitution
6. 6. Distribution Property
7. 7. Segment addition
8. a2 � b2 � c2 8. Substitution
A
a b
d e
c
B
C
D
Chapter 7 40 Glencoe Geometry
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
7-5C
opyright ©G
lencoe/McG
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Short Leg
Long Leg
Hypotenuse
05-42 Geo-07-873964 4/12/06 8:45 PM Page 40
Chapter 7 41 Glencoe Geometry
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Spreadsheet ActivityFractals
NAME ______________________________________________ DATE ____________ PERIOD _____
7-5
You can use a spreadsheet to create a Sierpinski triangle.
Use a spreadsheet to create a Sierpinski triangle.
Step 1 In cell A2, enter 1. In cell A3, enter an equals sign followed by A2�1 . This willreturn the number of iterations. Click on the bottom right corner of cell A2 anddrag it through cell A500 to get 500 iterations.
Step 2 In cell B1, enter 0.5. This indicates the midpoints of the segments.Step 3 In cell C1, enter 1 and in cell D1, enter 0.3.Step 4 In cell B2, enter an equals sign followed by 3*RAND(). Click on the bottom right
corner of cell B2 and drag in through cell B500 to get 500 iterations.Step 5 In cell C2, enter an equals sign followed by the recursive formula
IF(B2<1,(1�$B$1)*C1,IF(B22,(1�$B$1)*C1�$B$1,(1�$B$1)*C1�2*$B$1)). Thiswill return the x values of the points to be graphed. Click on the bottom right corner of cell C2 and drag through cell C500.
Step 6 In cell D2, enter an equals sign followed by the recursive formulaIF(B21,(1�$B$1)*D1,IF(B22,(1�$B$1)*D1�$B$1,(1�$B$1)*D1)). This willreturn the y values of the points to be graphed. Click on the bottom right corner ofcell D2 and drag throughcell D500.
Step 7 To graph the values incolumns C and D, first highlight all of the data in the two columns. Next,choose the chart wizardfrom the toolbar. Select XY(Scatter). Press Next, Next.Then select the Gridlinestab and uncheck the Major gridlines. Then press Next and Finish.This will return the Sierpinski triangle.
Analyze your drawing.1. What happens to your drawing if you have more iterations? Try 1000, 2000, and 5000.
2. Change the 0.5 to 2\3 in cell B1. (Hint: You may need to enter 0.666666 for 2\3.) Howdoes this change the picture?
3. Change 0.3 to 0.6 in cell D1. How does this change the drawing? 4. Enter the following into a new spreadsheet and describe what you see.
Step 1: In cell A2, enter the formula � A1.Step 2: In cell B2, enter the formula � A1�B1.Step 3: Click on the bottom right corner of cell B2 and drag through cell L2.Step 4: First, click on the 2 next to cell A2. Then, click on the bottom left corner of 2
and drag down through cell 12.Step 5: In cell A1, enter a 1 and press ENTER.
Sheet 1 Sheet 2 Sheet 3
Less
on
7-5
Example
Exercises
05-42 Geo-07-873964 4/12/06 8:45 PM Page 41
05-42 Geo-07-873964 4/12/06 8:45 PM Page 42
Chapter 7 43 Glencoe Geometry
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Student Recording SheetUse this recording sheet with pages 428–429 of the Student Edition.
NAME ______________________________________________ DATE ____________ PERIOD _____
7
1.
2.
3. Record your answer and fill in thebubbles in the grid below. Be sure to use the correct place value.
4.
5.
6. Record your answer and fill in thebubbles in the grid below. Be sure to use the correct place value.
7.
8.
9.
10.
11.
12.
Record your answers for Question 13on the back of this paper.
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
.
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
F G H J
A B C D
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
.
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
F G H J
A B C D
Read each question. Then fill in the correct answer.
Ass
essm
ent
Pre-AP
SCORE _____
Chapter 7 44 Glencoe Geometry
Rubric for Scoring Pre-AP(Use to score the Pre-AP question on page 429 of the Student Edition.)
NAME ______________________________________________ DATE ____________ PERIOD _____
7C
opyright ©G
lencoe/McG
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ompanies, Inc.
General Scoring Guidelines
• If a student gives only a correct numerical answer to a problem but does not showhow he or she arrived at the answer, the student will be awarded only 1 credit.All extended-response questions require the student to show work.
• A fully correct answer for a multiple-part question requires correct responses forall parts of the question. For example, if a question has three parts, the correctresponse to one or two parts of the question that required work to be shown is notconsidered a fully correct response.
• Students who use trial and error to solve a problem must show their method.Merely showing that the answer checks or is correct is not considered a completeresponse for full credit.
Exercise 13 Rubric
Score Specific Criteria
4 An understanding that �ADE � �ADE is shown by using the TriangleProportionality Theorem, which states that if a line is parallel to one side of a triangle and intersects the other two sides in two distinct points,then it separates these sides into segments of proportional length, so
�AA
EC� � �
AA
DB�. Since the corresponding sides are proportional and the
included angle, �A, is the same, by the SAS Similarity Theorem we knowthat the triangles are similar. The correct proportion is set up in part b todetermine whether the missing value is 800 ft or 2000 ft.
3 A generally correct solution, but may contain minor flaws in reasoning or computation.
2 A partially correct interpretation and/or solution to the problem.
1 A correct solution with no evidence or explanation.
0 An incorrect solution indicating no mathematical understanding of theconcept or task, or no solution is given.
SCORE _____
Chapter 7 45 Glencoe Geometry
Chapter 7 Quiz 1(Lessons 7–1 and 7–2)
NAME ______________________________________________ DATE ____________ PERIOD _____
7
Ass
essm
ent
SCORE _____Chapter 7 Quiz 2(Lesson 7–3)
NAME ______________________________________________ DATE ____________ PERIOD _____
7
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1.
2.
3.
4.
5.
1. GARDENS The model of a circular garden is 8 inches indiameter. The actual garden will be 20 feet in diameter. Findthe ratio of the diameter of the model to the diameter of theactual garden.
2. PHOTOS A 4-inch by 6-inch photograph, set vertically, isenlarged to make a poster 22 inches wide. How tall is the poster?
3. Are any of the three trianglessimilar? If so, write theappropriate similaritystatement.
4. If �ABC � �DEC, find x and the scale factor of �ABC to �DEC.
5. MULTIPLE CHOICE In a rectangle, the ratio of the length tothe width is 5:2, and its perimeter is 126 centimeters. Find thewidth of the rectangle.A. 9 cm B. 18 cm C. 45 cm D. 50.4 cm
D
E
CB
A
20
253x � 2
2x
BP X Y
Z
Q
R
A
C
5
4 8 8 8
10
4
1.
2.
3.
4.
5.
For Questions 1 and 2, determine whether each pair oftriangles is similar. Justify your answer.
1. 2.
3. Identify the similar triangles in the figure,then find x.
4. SHADOWS A person who is 5 feet tall casts a shadow that is4 feet long. At the same time, a flagpole casts a shadow that is18 feet long. Find the height of the flagpole.
5. Find x in the figure.
46
9 x
8
A
B D
EF
C 4
6x
20
15
98
10 1241�
52�41�
87�
SCORE _____
Chapter 7 46 Glencoe Geometry
Chapter 7 Quiz 3(Lesson 7–4)
NAME ______________________________________________ DATE ____________ PERIOD _____
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opyright ©G
lencoe/McG
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ompanies, Inc.
SCORE _____Chapter 7 Quiz 4(Lesson 7–5)
NAME ______________________________________________ DATE ____________ PERIOD _____
7
1.
2.
3.
4.
5.
1. Determine whether M�N� || K�L�.Justify your answer.
2. Find x so that L�M� || A�B�.
3. In �ABC, D�E� is parallel to A�C� and DE � 10. Find the length of A�C� if D�E� is the midsegment of �ABC .
4. Find DE.
5. A triangle QRS has vertices Q(�2, 3), R(�2, �3), and S(8, 1).TU is the midsegment of QRS and is parallel to QR. What arethe coordinates of T and U?
20
12
15 DE
B
A
C
6 8
4A B
C
L Mx
J
M
N11
2
3
9
L
K
1.
2.
3.
4.
5.
1. If �PQR � � XYZ, find the perimeter of �XYZ.
For Questions 2–4, refer to the trianglesABC and DEF. �ABC � �DEF. Theperimeter of �ABC is 48 cm and theperimeter of �DEF is 32 cm.
2. Find the length of D�E� to the nearesttenth.
3. What is the relationship between the corresponding altitudes B�X� and E�Y�?
4. Find the length of E�Y� to the nearesttenth.
5. In �RST, TU��� bisects �T. If U is a point on R�S�, RU � 6,RT � 9, and ST � 12, find RS.
D F
E
Y
A C
B
128
X
16
128
P R
Q
5
X Z
Y
SCORE _____
Chapter 7 47 Glencoe Geometry
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Chapter 7 Mid-Chapter Test(Lessons 7–1 through 7–3)
NAME ______________________________________________ DATE ____________ PERIOD _____
7
Ass
essm
ent
1. Polygon ABCD is similar to polygon PQRS. Which proportion must be true?
A. �AA
DC� � �
PP
QS� B. �C
BDC� � �
QR
RS� C. �B
ADB� � �Q
PQR� D. �
CA
DB� � �
PR
QS�
2. This fall, 126 students participated in the soccer program, while 54 playedvolleyball. What was the ratio of soccer players to volleyball players?
F. �34� G. �
37� H. �
43� J. �
73�
3. The ratio of the measures of the angles of a triangle is 2:3:10. What is theleast angle measure?A. 12 B. 15 C. 24 D. 36
4. Find x.F. 2 H. 6G. 4.8 J. 6.4
5. Rectangle ABCD � rectangle EFGH, the perimeter of ABCD is 54 centimeters,and the perimeter of EFGH is 36 centimeters. What is the scale factor ofABCD to EFGH?
A. �23� B. �
32� C. �
35� D. �
53�
10 8
x
D
E
AC B18
6.
7.
8.
9.
10.
1.
2.
3.
4.
5.
Part II
For Questions 6 and 7, determine whether each pair oftriangles is similar. Justify your answer.
6. 7.
8. If �ABE � �BCD, find DE and the scale factor of �ABE to �BCD.
9. Quadrilateral ABCD � quadrilateral RSUV, m�ABC � 120,and the scale factor of ABCD to RSUV is �
85�. Find m�RSU.
10. MODELS Sasha made a model of a clipper ship. Her modelhas a length of 18 inches, and the original ship has a length of160 feet and a width of 32 feet. Find the width of the modelship.
24 32
9
A
B ED
C
45251810 85�85�6
415
10
Part I Write the letter for the correct answer in the blank at the right of each question.
SCORE _____
Chapter 7 48 Glencoe Geometry
Chapter 7 Vocabulary Test
NAME ______________________________________________ DATE ____________ PERIOD _____
7C
opyright ©G
lencoe/McG
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ill, a division of The M
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-Hill C
ompanies, Inc.
Choose the correct term to complete each sentence.
1. If there are 15 girls and 9 boys in an art class, the (ratio orscale factor) of girls to boys in the class is 5:3.
2. If �ABC � �DEF, AB �10, and DE � 2.5, then the (scalefactor or proportion) of �ABC to �DEF is 4:1.
Choose from the terms above to complete the sentence.
3. In �LMN, P lies on L�M� and Q on L�N�. If PQ � �12�MN, P�Q� is
called a(n) .
4. The product of the in the equation �3x� � �
2340� is 90.
5. The product of the in the equation �3x� � �
2340� is 24x.
State whether each sentence is true or false. If false,replace the underlined word or number to make a truesentence.
6. If quadrilaterals ABCD and WXYZ have corresponding anglescongruent and corresponding sides proportional, they arecalled .
7. The equation �3x� � �
2340� is called a(n) .
8. In a proportion, the cross products of the equals thecross product of the means.
Describe each phrase in your own words.
9. equality of cross products
10. midsegment
extremes
scale factor
cross products
?
?
?
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
cross productsextremesmeans
midsegmentproportionratio
scale factorsimilar polygons
SCORE _____
Chapter 7 49 Glencoe Geometry
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Chapter 7 Test, Form 1NAME ______________________________________________ DATE ____________ PERIOD _____
7
Ass
essm
entWrite the letter for the correct answer in the blank at the right of each question.
1. There are 15 plums and 9 apples in a fruit bowl. What is the ratio of apples toplums?A. 3:5 B. 3:8 C. 5:3 D. 8:3
2. The scale drawing of a porch is 8 inches wide by 12 inches long. If the actualporch is 12 feet wide, what is the length of the porch?F. 8 ft G. 10 ft H. 16 ft J. 18 ft
3. Solve �56� � �
4x�.
A. 4.6 B. 4.8 C. 5 D. 7
4. A quality control technician checked a sample of 30 bulbs. Two of the bulbswere defective. If the sample was representative, find the number of bulbsexpected to be defective in a case of 450.F. 24 G. 30 H. 36 J. 45
5. Find the triangle similar to �ABC at the right.A. C.
B. D.
6. Find x if �ABC � �JKL.F. 10 H. 25G. 14 J. 29
7. Quadrilateral ABCD � quadrilateral PQRS. If AB � 10, BC � 6, PS � 12,and QR � 4, find the scale factor of ABCD to PQRS.
A. �12� B. �
32� C. �
53� D. �
56�
8. Quadrilateral ABCD � quadrilateral EFGH.Find x.F. 15 H. 25G. 20 J. 30
9. Which theorem or postulate can be used to prove that these two triangles are similar?A. AA B. SAS C. SSA D. SSS
10. Find MN.
F. 5�13� G. 6 �
34� H. 7 J. 12
35�8
96
35�
Q
PM
L
N
6
84
27�
63�
B
C
D
A
F
E
H
G 60� 120�80�
100�4x �
A C
B J L
K186 9
x � 2
4
35
15
36
39
2210
24
5
12
35
12
13
CB
A
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Chapter 7 50 Glencoe Geometry
Chapter 7 Test, Form 1 (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
7C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
11.
12.
13.
14.
15.
16.
17.
18.
19.
11. A 5-foot tall student cast a 4-foot shadow. If the tree next to her cast a 44-footshadow, what is the height of the tree?
A. 35�15� ft B. 45 ft C. 51�
12� ft D. 55 ft
12. In �ABC, D�E� || A�C�. If AD � 12, BD � 3, and CE � 10,find BE.F. 1 H. 2
G. 1�12� J. 2�
12�
13. In �ABC A�C� || M�N�. What is x?A. 8 C. 25B. 10 D. 29
14. Find x.F. 14 H. 16G. 15 J. 18
15. �FGH � �PQR, FG � 6, PQ � 10, and the perimeter of �PQR is 35. What isthe perimeter of �FGH?A. 21 B. 27 C. 31 D. 58�
13�
16. �LMN � �XYZ with altitudes K�L�and W�X�. Find KL.F. 6 H. 9G. 7 J. 19
17. Find x.A. 5 C. 6�
12�
B. 6 D. 7�12�
18. Find x.F. 16 H. 20G. 18 J. 21
19. Nathan is building a model of his father’s sailboat with a scale factor of �312�.
The actual sail is in the shape of a right triangle with a base of 8 meters anda hypotenuse of 13 meters. What will be the approximate perimeter of the sailon the model boat?A. 32 cm B. 48.81 cm C. 65.62 cm D. 97.65 cm
Bonus In �ABC, AB � 10, BC � 16, D�E� ⊥ A�C�,and DE � 6. Find CD. 10
6B C
D
E
A
16
15
1824
x
1610
129x
28 123
K
L X
M YWZN
1610
24x
C B
A
N
M12
18
163x
C B
A
E
D12
10
3
B:
SCORE _____
Chapter 7 51 Glencoe Geometry
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Chapter 7 Test, Form 2ANAME ______________________________________________ DATE ____________ PERIOD _____
7
Ass
essm
entWrite the letter for the correct answer in the blank at the right of each question.
1. Of the 240 students eating lunch, 96 purchased their lunch and the restbrought a bag lunch. What is the ratio of students purchasing lunch tostudents bringing a bag lunch?A. 2:3 B. 2:5 C. 3:2 D. 5:2
2. In a rectangle, the ratio of the width to the length is 4:5. If the rectangle is 40 centimeters long, find its width.F. 32 cm G. 36 cm H. 44 cm J. 50 cm
3. A postage stamp 25 millimeters wide and 40 millimeter tall is enlarged tomake a poster. The poster is 4 feet wide. Find the height of the poster.A. 2.5 ft B. 5.25 ft C. 5.8 ft D. 6.4 ft
4. Find the polygon that is similar to ABCD.F. H.
G. J.
5. If �PQR � �STU, find x.A. 4.4 C. 24.6B. 7 D. 35
6. If ABCD � EFGH, find x.F. 18.75 H. 22.75G. 20 J. 28
7. �ABC � �LMN, AB � 18, BC � 12, LN � 9, and LM � 6. What is the scalefactor of �ABC to �LMN?
A. �92� B. �
32� C. �
31� D. �
21�
8. Name the theorem or postulate that can be used to prove that these triangles are similar.F. AA Similarity H. SAS SimilarityG. SSS Similarity J. SSA Similarity
For Questions 9 and 10, refer to the figure at the right.9. Identify the true statement.
A. �PQR � �RST C. �PQR � �TSRB. �PQR � �STR D. �PQR � �TRS
10. Find x.
F. 2�12� G. 3 H. 3�
12� J. 4
15
18
4x2
21–2
3
T
R
P
Q
S
14
43
7
16
30
10
x � 4
A
BC
DE H
GF
22�123�
5x�12 8
4.5
R U
S
TQ
P
88
2–3
2
2 618
6
4
12
A D
B C
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Chapter 7 52 Glencoe Geometry
Chapter 7 Test, Form 2A (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
7C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
11.
12.
13.
14.
15.
16.
17.
18.
11. A 24-foot flagpole cast a 20-foot shadow. The building next to it cast an 85-footshadow. Find the height of the building.
A. 70�56� ft B. 89 ft C. 96�
16� ft D. 102 ft
12. Find QT.F. 15 H. 19G. 17 J. 21
13. Find x so that S�T� || P�R�.A. 4 C. 6
B. 4�12� D. 6�
12�
14. Find y.
F. �43� H. �
73�
G. 2 J. 3
15. If �KLM � �XYZ, find the perimeter of �XYZ.A. 40 C. 45B. 42 D. 48
16. �ABC � �JKL with altitudes B�X� and K�Y�.Find BX.F. 19.2 H. 24.6G. 21 J. 28
17. Find x.A. 4 C. 6B. 5 D. 8
18. Find y.
F. 2�14� H. 3�
12�
G. 2�34� J. 4�
12�
Bonus Find x.12
4 x
6
8
y
DA C
B
6S
Q
P R
12 8
x � 2 x
32
X CA
B10 6
Y LJ
K
9
X Z
Y4
K M
L7
9
69
2y
1–3y � 2
25
5
34x � 3 QR
P
S
T
24
40
35 RQ
PS
T
B:
SCORE _____
Chapter 7 53 Glencoe Geometry
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Chapter 7 Test, Form 2BNAME ______________________________________________ DATE ____________ PERIOD _____
7
Ass
essm
entWrite the letter for the correct answer in the blank at the right of each question.
1. Given the choice between doing an oral and a written report, 18 of the 28 students chose to do an oral report. Find the ratio of written to oral reports.A. 5:9 B. 9:5 C. 9:14 D. 14:9
2. A model of a lighthouse has diameter 8 inches and height 18 inches. If theactual diameter of the lighthouse is 20 feet, find its actual height.F. 30 ft G. 35 ft H. 45 ft J. 50 ft
3. The three sides of a triangle are in the ratio 2:4:5. If the shortest side of thetriangle is 4 meters long, find the perimeter.A. 17 m B. 22 m C. 32 m D. 40 m
4. Find the polygon that may be similar to ABCD.F. H.
G. J.
5. If �ABC � �DEF, find m�C.A. 54 C. 67B. 59 D. 69
6. Quadrilateral JKLM � quadrilateral WXYZ, JK � 15, LM � 10, XY � 6, andWX � 9. Find KL.F. 8 G. 10 H. 11 J. 12
7. �LMN � �RST, LN � 21, MN � 28, and the scale factor of �RST to �LMNis �
43�. Find ST.
A. 15�34� B. 21 C. 28 D. 37�
13�
8. Name the theorem or postulate that can be used to prove that these triangles are similar.F. AA Similarity H. SSA SimilarityG. SAS Similarity J. SSS Similarity
For Questions 9 and 10, refer to the figure at the right.9. Identify the similar triangles.
A. �LMN � �MPQ C. �LMN � �QPMB. �LMN � �QMP D. �LMN � �PQM
10. Find LM.F. 16 G. 17 H. 18 J. 20
1510 12
L
N
MP
Q
20
8
11.228
54�67�67�
DECA
FB
30
24
8
17
14
6
22
18
6
12
15
5
12
15
54
A B
D C
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Chapter 7 54 Glencoe Geometry
Chapter 7 Test, Form 2B (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
7C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
11.
12.
13.
14.
15.
16.
17.
18.
11. A 6-foot tall fence post cast a 2�12�-foot shadow. A nearby clock tower cast a
35-foot shadow. What is the height of the tower?A. 37�
12� ft B. 71 ft C. 78 ft D. 84 ft
12. Find CE.F. 25 H. 27G. 26 J. 28
13. Find FH so that G�H� || D�E�.A. 4 C. 6B. 5 D. 7
14. Find x.F. 4 H. 9G. 6 J. 12
15. If �ABC � �PQR, find the perimeter of �PQR.
A. 12 C. 14�12�
B. 13�12� D. 16
16. �ABC � �XYZ with altitudes A�P�and X�Q�. Find AP.
F. 11�14� H. 15�
14�
G. 14 J. 20
17. Find x.A. 7 C. 9B. 8 D. 10
18. Find y.
F. 3�34� H. 6
G. 4 J. 7�12�
Bonus Find CE.6
5
4
39
A
B
C
D
E
6
21–4
16
y
R T
SU
40
16
x � 2
3x
125
Q
X
Y Z27
P
A
B C
6 Q
R
P8
7 3
B
C
A
58
2x
x � 3
9
10
15D
G
FE H
8
20
EB C
DA
35
B:
SCORE _____
Chapter 7 55 Glencoe Geometry
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Chapter 7 Test, Form 2CNAME ______________________________________________ DATE ____________ PERIOD _____
7
Ass
essm
ent1. Of the 300 television sets sold at an electronics store last
month, 90 were flat-screen TVs. What is the ratio of flat-screenTVs to other TVs sold last month?
2. Determine whether �ABC � �DEF. Justify your answer.
3. When a 5-foot vertical pole casts a 3-foot, 4-inch shadow, anoak tree casts a 20-foot shadow. Find the height of the tree.
4. Quadrilateral ABCD � quadrilateral WXYZ, AB � 15, BC � 27,BC � 27, and the scale factor of WXYZ to ABCD is �
23�. Find XY.
5. The blueprint for a swimming pool is 8 inches by 2�12� inches.
The actual pool is 136 feet long. Find the width of the pool.
6. Find CD.
7. If quadrilateral ABCD � quadrilateral PQRS, find BC.
8. Determine whether �ABC � �DEF. Justify your answer.
9. �ABC � �XYZ, AB � 12, AC � 16, BC� 20, and XZ � 24.Find the perimeter of �XYZ.
For Questions 10 and 11, use the figure.
10. Identify the similar triangles.
11. Find x.
15 2x � 4
x6
P
Q
R S
T
9
8
6
42
5
B
EF
DC
A
28
10 6.5R
S P
Q B
A
C
D
1.8
2.46C EG
FD
22.5
15 1510
A
B
C DE
F
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Chapter 7 56 Glencoe Geometry
Chapter 7 Test, Form 2C (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
7C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
12. If �ABC � �PQR and B�M� and Q�N� are medians, find BM.
13. The ratio of the measures of the three sides of a triangle is 3:4:6.If the perimeter is 91, find the measure of the longest side.
14. If �RST � �UVW, find m�W.
15. In �ABC, A�X� bisects �BAC. Find x.
16. Find y so that M�N� || B�C�.
17. �ABC � �LMN, and A�D� and L�P� are altitudes. Find AD.
18. Find x.
Bonus Find EG.18
10
12
B
F
D EG
C
A
28
818
2x � 2
13.5
3620
8D
A
C B M P
L
N
18
8y4
y
B
CAN
M
4x � 5
2x
8
6
A C
X
B
85�
48�R T
S
U W
V
11
4.43.8
A C P R
Q
B
M N
12.
13.
14.
15.
16.
17.
18.
B:
SCORE _____
Chapter 7 57 Glencoe Geometry
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Chapter 7 Test, Form 2DNAME ______________________________________________ DATE ____________ PERIOD _____
7
Ass
essm
ent1. Of the 112 students in the marching band, 35 were in the
drum section. What is the ratio of drummers to othermusicians in the band?
2. Determine whether quadrilateral ABCD � quadrilateralEFGH. Justify your answer.
3. When a 9-foot tall garden shed cast a 5-foot, 3-inch shadow, ahouse cast a 28-foot shadow. Find the height of the house.
4. �ABC � �FGH, AB � 24, AC � 16, GH � 9, and FH � 12.Find the scale factor of �ABC to �FGH.
5. The model of a suspension bridge is 18 inches long and 2 inchestall. If the length of the actual bridge is 1650 feet, find its height.
6. Find GP.
7. If �JKL � �PQR, find x.
8. Determine whether �ABC � �PQR. Justify your answer.
9. �ABC � �PQR, AB � 18, BC � 20, AC � 22, and QR � 25.Find the perimeter of �PQR.
For Questions 10 and 11, use the figure.
10. Identify the similar triangles.
11. Find MN.20
x
6
Y Z
X
M
N
16
20
22.5
3012
158
P
BC
A
Q
R
35
14
6
x
J L
PQ
R
K
2.73.3
4.5
F H
Q
G
P
A
9
7
14 17
9 8.5
13.512
B
C
D H G
FE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Chapter 7 58 Glencoe Geometry
Chapter 7 Test, Form 2D (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
7C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
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-Hill C
ompanies, Inc.
12. If �FGH � �LMN and A�F� and B�L� are medians, find BL.
13. The ratio of the measures of the three angles of a triangle is3:4:8. Find the measure of the largest angle.
14. If quadrilateral DEFG � quadrilateral WXYZ, find m�Y.
15. In �PQR, Q�S� bisects �PQR. Find x.
16. Find x so that P�Q� || F�H�.
17. If �FGH � �JKL, find GX.
18. Find y.
Bonus Find FG.
2.8 3.2 4.2
8 7
A
B F
GEC
D
42 2y
12 16
X Y
K
F H JL
27 12 21–2
G
63
3x2x � 1
F H
Q
G
P
P Q
R
S3x � 1
32
40
2x � 3
E F Z W
XY
GD
68� 85�
82�125�
16.8 4.8
7.7
F H L
MB
N
G
A
12.
13.
14.
15.
16.
17.
18.
B:
SCORE _____
Chapter 7 59 Glencoe Geometry
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Chapter 7 Test, Form 3NAME ______________________________________________ DATE ____________ PERIOD _____
7
Ass
essm
ent1. In an orchard of apple and peach trees, �
37� of the trees are
peaches. What is the ratio of apple trees to peach trees?
2. Determine whether trapezoid ABCD � trapezoid PQRS.Justify your answer.
3. In �ABC, m�A � 51, AB � 14, and AC � 20. In �DEF,m�D � 51, DE � 16.8, and DF � 24. Determine whether�ABC � �DEF. Justify your answer.
4. A painting that is 48 inches by 12 inches is reduced to fit onan area that is 30 centimeters by 10 centimeters. Find themaximum dimensions of the reduced painting.
5. Find x.
6. If �ABC � �XYZ, find y.
7. The ratio of the measures of the sides of a triangle is 2:5:6. Ifthe length of the longest side is 48 inches, find the perimeter.
8. Find m�I.
9. �ABC � �DEF, AB � 8, BC � 13, AC � 15, and DF � 20.Find the perimeter of �DEF.
10. �ABC � �JKL, AB � 12, BC � 18.4, KL � 6.9, and JL � 5.6.Find the scale factor of �ABC to �JKL.
11. Find y.y � 8
4y � 7
F
G
HI
J45�
53�
17.5A C
B
2y
14X Z
Yy � 3
6
4.8
6.5K L
J
N
M
2x
9.6
15.6
12.47.8
9
15
6
23.4D
R S
PQ
C
A
B
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Chapter 7 60 Glencoe Geometry
Chapter 7 Test, Form 3 (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
7C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
12. Find SR.
For Questions 13 and 14, �FGH � �JKL.
13. Find x.
14. Find the ratio of the perimeter of �FGH to the perimeter of �JKL.
15. Find AD so that D�E� || A�B�.
16. Find the fourth iterate of the expression 3x � 1, where xinitially equals 0.8.
17. When a 15-foot tall climbing wall cast a 20-foot shadow, abuilding cast a 32-foot shadow. Find the height of the building.
18. If �ABC � �EFG and B�D� and F�H� are medians, find BD.
Bonus The ratio of the lengths of the sides of �ABC is 5:2.5:4. The scale factor of �ABC to �DECis 5:2, and the scale factor of�DEC to �FEG is 1:4. B�C� is the shortest side and A�B� is thelongest side of �ABC. Find FG.
10
A
B C
D E
G
F
HE G
F2x � 5
751–4
x � 5
DA C
B
A B
ED
C
2x � 4 3x
8x5x
12x
F H
G7.5
4.5
J L
K
30 12Q
RPS
40
12.
13.
14.
15.
16.
17.
18.
B:
SCORE _____
Chapter 7 61 Glencoe Geometry
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Chapter 7 Extended-Response TestNAME ______________________________________________ DATE ____________ PERIOD _____
7
Ass
essm
entDemonstrate your knowledge by giving a clear, concise solution to
each problem. Be sure to include all relevant drawings and justifyyour answers. You may show your solution in more than one way orinvestigate beyond the requirements of the problem.
1. Write a possible proportion if the extremes are 3 and 10.
2. �ABC and �WXY are isosceles triangles.
a. Write a possible ratio for the sides of �ABC if its perimeter is 42 inches.
b. Name possible measures for the sides of �ABC using your answer toPart a.
c. If �WXY has a perimeter of 28 and �ABC has sides with the measuresyou gave in Part b, what must be the measure of the sides of �WXY sothat �WXY � �ABC?
3. Write as many triangle similarity statements as possible for the figurebelow. How do you know that these triangles are similar?
4. Sketch two triangles that are not similar, but have one pair of correspondingangles congruent and two pairs of corresponding sides proportional. Labelthe corresponding angles and the proportional sides.
5.
a. Draw �XYZ inside �PQR with half the perimeter of �PQR. Explainyour process and why it works.
b. Draw the figure that results when your process in Part a is iterated 3 times.
c. Explain why your figure in Part b is a fractal.
d. The perimeter of �PQR is �12�x. If x equals 96, what is the perimeter of
the smallest triangle in your figure in Part b?
P R
Q
A B C D
I E
F
G
H
SCORE _____
Chapter 7 62 Glencoe Geometry
Standardized Test Practice(Chapters 1–7)
NAME ______________________________________________ DATE ____________ PERIOD _____
7C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
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ompanies, Inc.
1. Find the length of Y�Z�. (Lesson 1-2)
A 1.9 in. C 7.2 in.B 5.3 in. D 12.5 in.
2. Given: 3b � 4 � 16 Conjecture: b � 0Which of the following would be a counterexample? (Lesson 2-1)
F b � �1 G b � 0 H b � 3.5 J b � 4
3. Find the plane that is parallel to plane PTU. (Lesson 3-1)
A plane QRU C plane PQSB plane QRS D plane SPU
4. Find m�1. (Lesson 3-2)
F 5 H 41G 12 J 44
5. Which statement must be true in order to prove �ABC � �DCB by SAS? (Lesson 4-4)
A C�B� bisects �ABD.B �BCA � �CBDC �BDC � �CABD A�B� � B�C�
6. In an indirect proof, you assume that the conclusion is false andthen find a(n) . (Lesson 5-3)
F assumption H truth valueG contradiction J conditional statement
7. Demont and Tony are competing to see whose house is the tallest.Early in the afternoon, Tony, who is 4 feet tall, measured his shadowto be 9.6 inches and the shadow of his house to be 62.4 inches. Laterin the day, Demont, who is 5 feet tall, measured his shadow to be15.6 inches and the shadow of his house to be 62.4 inches. Who livesin the taller house? (Lesson 7-3)
A DemontB Both houses are the same height.C TonyD There is not enough information.
?
D
A C
B
(3x � 5)�
(125 � 7x)�
1
R
P
Q
STU
X Z5.5 in.
3.6 in. Y
Part 1: Multiple Choice
Instructions: Fill in the appropriate circle for the best answer.
1.
2.
3.
4.
5.
6.
7. A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
Chapter 7 63 Glencoe Geometry
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Standardized Test Practice (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
7
Ass
essm
ent8. Find the coordinates of the midpoint of AB for A(�24, 15) and
B(13, �31). (Lesson 1-3)
F (�18.5, �23) G (�11, �16) H (�5.5, �8) J (10.5, 23)
For Questions 9 and 10, use the figure at the right.
9. The perimeter of rectangle DEFG is 176, EF � h, and DE � 7h. What is h? (Lesson 1-6)
A 11 C 22B 15 D 77
10. What is the area of the rectangle DEFG? (Lesson 1-6)
F 88 units2 G 225 units2 H 513 units2 J 847 units2
11. What is the slope-intercept form for the line y � 7 � 4(x�10)?(Lesson 3-4)
A y � 4x � 47 B 4x � y � 47 C 4x � y � 17 D 4�xy� � 17
12. Which of the following is the equation of a line parallel to the linepassing through (4, �3) and (8, 5)? (Lesson 3-3)
F y � x � 2 G 2y � 9x � 4 H 2y � 2x � 4 J y � 2x � 9
D E
G F
8.
9.
10.
11.
12. F G H J
A B C D
F G H J
A B C D
F G H J
13. Find m�2. (Lesson 3-2)
14. �LMN is equilateral, LM is one more than threetimes a number, MN is nine less than five times thenumber, and NL is eleven more than the number.Find LM. (Lesson 4-1)
52�
12 34
Part 2: Griddable
Instructions: Enter your answer by writing each digit of theanswer in a column box and then shading in the appropriate circlethat corresponds to that entry.
13.
14.
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
.
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
.
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
Chapter 7 64 Glencoe Geometry
Standardized Test Practice (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
7C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
Part 3: Short Response
Instructions: Write your answers in the spaces provided.
15. Solve ��4106
� � �4x �
510
�. (Lesson 7-1)
16. X�A� is an altitude of �XYB. Find y.(Lesson 5-1)
17. Two sides of a triangle measure 21 inches and 32 inches, andthe third side measures x inches. Find the range for x. (Lesson 5-4)
18. If �ABC � �HIJ, find the perimeter of �HIJ. (Lesson 7-5)
19. Given T(3, �1), U(1, �7), V(8, �5), W(2, 6), X(�4, 8), and Y(�2, 1), determine whether �TUV � �WXY. Explain.(Lesson 4-3)
20. Given the points S(�5, 7), T(1, 9), P(12, �1), and R(3, 26):
a. Find the lengths of ST and PR to the nearest hundredth.(Lesson 3-6)
b. Determine the slope of ST and of PR. (Lesson 3-3)
c. Are ST and PR parallel, perpendicular, or neither? (Lesson 3-3)
32 cm
80 cm
60 cm
A B
C 12 cmH I
J
(2y � 81)� BA
X
Y
15.
16.
17.
18.
19.
20a.
20b.
20c.
Chapter 7 A1 Glencoe Geometry
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ht ©
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ncoe
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An
swer
s
Cha
pter
75
Gle
ncoe
Geo
met
ry
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Less
on R
eadi
ng G
uide
Pro
po
rtio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-1
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 7
-1 i
n y
our
text
boo
k.
Est
imat
e th
e ra
tio
of l
engt
h t
o w
idth
for
th
e ba
ckgr
oun
d re
ctan
gles
in
Tif
fan
y’s
Cle
mat
is S
kyli
ght.
Sam
ple
an
swer
:ab
ou
t 5
to 2
Rea
d t
he
Less
on
1.M
atch
eac
h d
escr
ipti
on i
n t
he
firs
t co
lum
n w
ith
a w
ord
or p
hra
se f
rom
th
e se
con
dco
lum
n.
a.T
he
rati
o of
tw
o co
rres
pon
din
g qu
anti
ties
ivi.
prop
orti
on
b.
ran
d u
in t
he
equ
atio
n �r s�
�� ut �
vii
.cro
ss p
rodu
cts
c.a
com
pari
son
of
two
quan
titi
esvi
iii.
mea
ns
d.
ruan
d st
in t
he
equ
atio
n �r s�
�� ut �
iiiv
.sc
ale
fact
or
e.an
equ
atio
n s
tati
ng
that
tw
o ra
tios
are
equ
ali
v.ex
trem
es
f.s
and
tin
th
e eq
uat
ion
�r s��
� ut �iii
vi.r
atio
2.If
m,n
,p,a
nd
qar
e n
onze
ro n
um
bers
su
ch t
hat
�m n��
�p q� ,w
hic
h o
f th
e fo
llow
ing
stat
emen
ts c
ould
be
fals
e?B
,C,E
A.
np
�m
qB
.�np �
�� mq �
C.
mp
�n
qD
.qm
�pn
E.
�m n��
� pq �F.
� pq ��
� mn �
G.m
:p�
n:q
H.m
:n�
p:q
3.W
rite
tw
o pr
opor
tion
s th
at m
atch
eac
h d
escr
ipti
on.
a.M
ean
s ar
e 5
and
8;ex
trem
es a
re 4
an
d 10
.
any
two
of
�4 5��
� 18 0�,�
4 8��
� 15 0�,�
1 50 ��
�8 4� ,�1 80 �
��5 4�
b.
Mea
ns
are
5 an
d 4;
extr
emes
are
pos
itiv
e in
tege
rs t
hat
are
dif
fere
nt
from
mea
ns.
any
two
of
�2 5��
� 14 0�,�
2 4��
� 15 0�,�
1 4��
� 25 0�,�
1 5��
� 24 0�,�
1 50 ��
�4 2� ,�1 40 �
��5 2� ,
�2 40 ��
�5 1� ,
or
�2 50 ��
�4 1�
Rem
emb
er W
hat
Yo
u L
earn
ed
4.S
omet
imes
it
is e
asie
r to
rem
embe
r a
mat
hem
atic
al i
dea
if y
ou p
ut
it i
nto
wor
ds w
ith
out
usi
ng
any
mat
hem
atic
al s
ymbo
ls.H
ow c
an y
ou u
se t
his
app
roac
h t
o re
mem
ber
the
con
cept
of
equ
alit
y of
cro
ss p
rodu
cts?
Sam
ple
an
swer
:Th
e p
rod
uct
of
the
mea
ns
equ
als
the
pro
du
ct o
f th
e ex
trem
es.
Lesson 7-1
Cha
pter
73
Gle
ncoe
Geo
met
ry
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Ant
icip
atio
n G
uide
Pro
po
rtio
ns
and
Sim
ilari
ty
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7
Bef
ore
you
beg
in C
ha
pte
r 7
•R
ead
each
sta
tem
ent.
•D
ecid
e w
het
her
you
Agr
ee (
A)
or D
isag
ree
(D)
wit
h t
he
stat
emen
t.
•W
rite
A o
r D
in
th
e fi
rst
colu
mn
OR
if
you
are
not
su
re w
het
her
you
agr
ee o
rdi
sagr
ee,w
rite
NS
(N
ot S
ure
).
Aft
er y
ou c
omp
lete
Ch
ap
ter
7
•R
erea
d ea
ch s
tate
men
t an
d co
mpl
ete
the
last
col
um
n b
y en
teri
ng
an A
or
a D
.
•D
id a
ny
of y
our
opin
ion
s ab
out
the
stat
emen
ts c
han
ge f
rom
th
e fi
rst
colu
mn
?
•F
or t
hos
e st
atem
ents
th
at y
ou m
ark
wit
h a
D,u
se a
pie
ce o
f pa
per
to w
rite
an
exam
ple
of w
hy
you
dis
agre
e.
STEP
1
STEP
2
ST
EP
1S
tate
men
tS
TE
P 2
A,D
,or
NS
A o
r D
1.R
atio
s ar
e al
way
s w
ritt
en a
s fr
acti
ons.
D2.
A p
ropo
rtio
n i
s an
equ
atio
n s
tati
ng
that
tw
o ra
tios
are
eq
ual
.A
3.T
wo
rati
os a
re i
n p
ropo
rtio
n t
o ea
ch o
ther
on
ly i
f th
eir
cros
s pr
odu
cts
are
equ
al.
A
4.If
�a b��
� dc � ,th
en �a c�
��d b� .
D
5.T
he
rati
o of
th
e le
ngt
hs
of t
he
side
s of
sim
ilar
fig
ure
s is
ca
lled
th
e sc
ale
fact
or f
or t
he
two
figu
res.
A
6.If
on
e an
gle
in a
tri
angl
e is
con
gru
ent
to a
n a
ngl
e in
an
oth
er t
rian
gle,
then
th
e tw
o tr
ian
gles
are
sim
ilar
.D
7.If
a li
ne is
par
alle
l to
one
side
of
a tr
iang
le a
nd in
ters
ects
th
e ot
her
two
side
s in
tw
o di
stin
ct p
oint
s,th
en t
he li
ne
sepa
rate
s th
e tw
o si
des
into
con
grue
nt s
egm
ents
.D
8.A
seg
men
t w
hos
e en
dpoi
nts
are
th
e m
idpo
ints
of
two
side
s of
a t
rian
gle
is p
aral
lel
to t
he
thir
d si
de o
f th
e tr
ian
gle.
A
9.If
tw
o tr
ian
gles
are
sim
ilar
th
en t
hei
r pe
rim
eter
s ar
e eq
ual
.D
10.
Th
e m
edia
ns
of t
wo
sim
ilar
tri
angl
es a
re i
n t
he
sam
e pr
opor
tion
as
corr
espo
ndi
ng
side
s.A
Chapter Resources
Answers (Anticipation Guide and Lesson 7–1)
Chapter 7 A2 Glencoe Geometry
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Cha
pter
77
Gle
ncoe
Geo
met
ry
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nued
)
Pro
po
rtio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-1
Use
Pro
per
ties
of
Pro
po
rtio
ns
A s
tate
men
t th
at t
wo
rati
os a
re e
qual
is
call
ed a
pro
por
tion
.In
th
e pr
opor
tion
�a b��
� dc � ,w
her
e b
and
dar
e n
ot z
ero,
the
valu
es a
and
dar
e th
e ex
trem
esan
d th
e va
lues
ban
d c
are
the
mea
ns.
In a
pro
port
ion
,th
e pr
odu
ct o
f th
em
ean
s is
equ
al t
o th
e pr
odu
ct o
f th
e ex
trem
es,s
o ad
�bc
.
�a b��
� dc �
a�
d�
b�
c↑
↑ex
trem
esm
eans
Sol
ve � 19 6�
��2 x7 �
.
� 19 6��
�2 x7 �
9 �
x�
16 �
27C
ross
pro
duct
s
9x�
432
Mul
tiply
.
x�
48D
ivid
e ea
ch s
ide
by 9
.
A r
oom
is
49 c
enti
met
ers
by
28 c
enti
met
ers
on a
sca
le
dra
win
g of
a h
ouse
.For
th
e ac
tual
roo
m,t
he
larg
er d
imen
sion
is
14 f
eet.
Fin
d t
he
shor
ter
dim
ensi
on o
f th
e ac
tual
roo
m.
If x
is t
he
room
’s s
hor
ter
dim
ensi
on,t
hen
�2 48 9��
� 1x 4�
49x
�39
2C
ross
pro
duct
s
x�
8D
ivid
e ea
ch s
ide
by 4
9.
Th
e sh
orte
r si
de o
f th
e ro
om i
s 8
feet
.
Sol
ve e
ach
pro
por
tion
.
1.�1 2�
��2 x8 �
562.
�3 8��
� 2y 4�9
3.�x x� �
2 22�
��3 10 0�
8
4.� 18
3 .2��
�9 y�54
.65.
�2x8�
3�
��5 4�
3.5
6.�x x
� �1 1
��
�3 4��
7
Use
a p
rop
orti
on t
o so
lve
each
pro
ble
m.
7.If
3 c
asse
ttes
cos
t $4
4.85
,fin
d th
e co
st o
f on
e ca
sset
te.
$14.
95
8.T
he
rati
o of
th
e si
des
of a
tri
angl
e ar
e 8:
15:1
7.If
th
e pe
rim
eter
of
the
tria
ngl
e is
48
0 in
ches
,fin
d th
e le
ngt
h o
f ea
ch s
ide
of t
he
tria
ngl
e.96
in.,
180
in.,
204
in.
9.T
he
scal
e on
a m
ap i
ndi
cate
s th
at o
ne
inch
equ
als
4 m
iles
.If
two
tow
ns
are
3.5
inch
esap
art
on t
he
map
,wh
at i
s th
e ac
tual
dis
tan
ce b
etw
een
th
e to
wn
s?14
mi
shor
ter
dim
ensi
on�
��
long
er d
imen
sion
Exam
ple
1
Exam
ple
2
Exer
cise
s
Lesson 7-1
Cha
pter
76
Gle
ncoe
Geo
met
ry
Stud
y G
uide
and
Inte
rven
tion
Pro
po
rtio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Wri
te R
atio
sA
rat
iois
a c
ompa
riso
n o
f tw
o qu
anti
ties
.Th
e ra
tio
ato
b,w
her
e b
is n
ot
zero
,can
be
wri
tten
as
�a b�or
a:b
.Th
e ra
tio
of t
wo
quan
titi
es i
s so
met
imes
cal
led
a sc
ale
fact
or.F
or a
sca
le f
acto
r,th
e u
nit
s fo
r ea
ch q
uan
tity
are
th
e sa
me.
In 2
002,
the
Ch
icag
o C
ub
s b
aseb
all
team
won
67
gam
es o
ut
of 1
62.
Wri
te a
rat
io f
or t
he
nu
mb
er o
f ga
mes
won
to
the
tota
l n
um
ber
of
gam
es p
laye
d.
To
fin
d th
e ra
tio,
divi
de t
he
nu
mbe
r of
gam
es w
on b
y th
e to
tal
nu
mbe
r of
gam
es p
laye
d.T
he
resu
lt i
s � 16 67 2�
,wh
ich
is
abou
t 0.
41.T
he
Ch
icag
o C
ubs
won
abo
ut
41%
of
thei
r ga
mes
in
200
2.
A d
oll
hou
se t
hat
is
15 i
nch
es t
all
is a
sca
le m
odel
of
a re
al h
ouse
wit
h a
hei
ght
of 2
0 fe
et.W
hat
is
the
rati
o of
th
e h
eigh
t of
th
e d
oll
hou
se t
o th
eh
eigh
t of
th
e re
al h
ouse
?T
o st
art,
con
vert
th
e h
eigh
t of
th
e re
al h
ouse
to
inch
es.
20 f
eet
�12
in
ches
per
foo
t �
240
inch
esT
o fi
nd
the
rati
o or
sca
le f
acto
r of
th
e h
eigh
ts,d
ivid
e th
e h
eigh
t of
th
e do
ll h
ouse
by
the
hei
ght
of t
he
real
hou
se.T
he
rati
o is
15
inch
es:2
40 i
nch
es o
r 1:
16.T
he
hei
ght
of t
he
doll
hou
se i
s � 11 6�
the
hei
ght
of t
he
real
hou
se.
1.In
th
e 20
05 M
ajor
Lea
gue
base
ball
sea
son
,Ale
x R
odri
quez
hit
48
hom
e ru
ns
and
was
at
bat
605
tim
es.F
ind
the
rati
o of
hom
e ru
ns
to t
he
nu
mbe
r of
tim
es h
e w
as a
t ba
t.
� 64 08 5�
2.T
her
e ar
e 18
2 gi
rls
in t
he
soph
omor
e cl
ass
of 3
05 s
tude
nts
.Fin
d th
e ra
tio
of g
irls
to
tota
l st
ude
nts
.
�1 38 02 5�
3.T
he
len
gth
of
a re
ctan
gle
is 8
in
ches
an
d it
s w
idth
is
5 in
ches
.Fin
d th
e ra
tio
of l
engt
h
to w
idth
.
�8 5�
4.T
he
side
s of
a t
rian
gle
are
3 in
ches
,4 i
nch
es,a
nd
5 in
ches
.Fin
d th
e sc
ale
fact
or b
etw
een
the
lon
gest
an
d th
e sh
orte
st s
ides
.
�5 3�
5.T
he
len
gth
of
a m
odel
tra
in i
s 18
in
ches
.It
is a
sca
le m
odel
of
a tr
ain
th
at i
s 48
fee
t lo
ng.
Fin
d th
e sc
ale
fact
or.
� 31 2�
Exam
ple
1
Exam
ple
2
Exer
cise
s
Answers (Lesson 7–1)
Chapter 7 A3 Glencoe Geometry
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
An
swer
s
Cha
pter
79
Gle
ncoe
Geo
met
ry
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Prac
tice
Pro
po
rtio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-1
1.N
UTR
ITIO
NO
ne o
unce
of
ched
dar
chee
se c
onta
ins
9 gr
ams
of f
at.S
ix o
f th
e gr
ams
of f
atar
e sa
tura
ted
fats
.Fin
d th
e ra
tio
of s
atur
ated
fat
s to
tot
al f
at i
n an
oun
ce o
f ch
eese
.
2:3
2.FA
RM
ING
Th
e ra
tio
of g
oats
to
shee
p at
a u
niv
ersi
ty r
esea
rch
far
m i
s 4:
7.T
he
nu
mbe
r of
sh
eep
at t
he
farm
is
28.W
hat
is
the
nu
mbe
r of
goa
ts?
16
3.A
RT
Edw
ard
Hop
per’
s oi
l on
can
vas
pain
tin
g N
igh
thaw
ksh
as a
len
gth
of
60 i
nch
es a
nd
a w
idth
of
30 i
nch
es.A
pri
nt
of t
he
orig
inal
has
a l
engt
h o
f 2.
5 in
ches
.Wh
at i
s th
e w
idth
of
the
prin
t?
1.25
in.
Sol
ve e
ach
pro
por
tion
.
4.�5 8�
�� 1x 2�
7.5
5.� 1.
x 12��
�1 5�0.
224
6.� 26 7x �
��4 3�
6
7.�x
� 32
��
�8 9��2 3�
8.�3x
4�5
��
�� 75 ��5 7�
9.�x
� 42
��
�x� 2
4�
�10
Fin
d t
he
mea
sure
s of
th
e si
des
of
each
tri
angl
e.
10.T
he
rati
o of
th
e m
easu
res
of t
he
side
s of
a t
rian
gle
is 3
:4:6
,an
d it
s pe
rim
eter
is
104
feet
.
24 f
t,32
ft,
48 f
t
11.T
he r
atio
of
the
mea
sure
s of
the
sid
es o
f a
tria
ngle
is 7
:9:1
2,an
d it
s pe
rim
eter
is 8
4 in
ches
.
21 in
.,27
in.,
36 in
.
12.T
he
rati
o of
th
e m
easu
res
of t
he
side
s of
a t
rian
gle
is 6
:7:9
,an
d it
s pe
rim
eter
is
77 c
enti
met
ers.
21 c
m,2
4.5
cm,3
1.5
cm
Fin
d t
he
mea
sure
s of
th
e an
gles
in
eac
h t
rian
gle.
13.T
he
rati
o of
th
e m
easu
res
of t
he
angl
es i
s 4:
5:6.
48,6
0,72
14.T
he
rati
o of
th
e m
easu
res
of t
he
angl
es i
s 5:
7:8.
45,6
3,72
15.B
RID
GES
Th
e sp
an o
f th
e B
enja
min
Fra
nkl
in s
usp
ensi
on b
ridg
e in
Ph
ilad
elph
ia,
Pen
nsy
lvan
ia,i
s 17
50 f
eet.
A m
odel
of
the
brid
ge h
as a
spa
n o
f 42
in
ches
.Wh
at i
s th
era
tio
of t
he
span
of
the
mod
el t
o th
e sp
an o
f th
e ac
tual
Ben
jam
in F
ran
klin
Bri
dge?
� 51 00�
Lesson 7-1
Cha
pter
78
Gle
ncoe
Geo
met
ry
Skill
s Pr
acti
ceP
rop
ort
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.FO
OTB
ALL
A t
igh
t en
d sc
ored
6 t
ouch
dow
ns
in 1
4 ga
mes
.Fin
d th
e ra
tio
of t
ouch
dow
ns
per
gam
e.
0.43
:1
2.E
DU
CA
TIO
NIn
a s
ched
ule
of
6 cl
asse
s,M
arta
has
2 e
lect
ive
clas
ses.
Wh
at i
s th
e ra
tio
of e
lect
ive
to n
on-e
lect
ive
clas
ses
in M
arta
’s s
ched
ule
?
1:2
3.B
IOLO
GY
Ou
t of
274
lis
ted
spec
ies
of b
irds
in
th
e U
nit
ed S
tate
s,78
spe
cies
mad
e th
een
dan
gere
d li
st.F
ind
the
rati
o of
en
dan
gere
d sp
ecie
s of
bir
ds t
o li
sted
spe
cies
in
th
eU
nit
ed S
tate
s.
� 13 39 7�
4.A
RT
An
art
ist
in P
ortl
and,
Ore
gon
,mak
es b
ron
ze s
culp
ture
s of
dog
s.T
he
rati
o of
th
eh
eigh
t of
a s
culp
ture
to
the
actu
al h
eigh
t of
th
e do
g is
2:3
.If
the
hei
ght
of t
he
scu
lptu
reis
14
inch
es,f
ind
the
hei
ght
of t
he
dog.
21 in
.
5.SC
HO
OL
Th
e ra
tio
of m
ale
stu
den
ts t
o fe
mal
e st
ude
nts
in
th
e dr
ama
clu
b at
Cam
pbel
lH
igh
Sch
ool
is 3
:4.I
f th
e n
um
ber
of m
ale
stu
den
ts i
n t
he
clu
b is
18,
wh
at i
s th
e n
um
ber
of f
emal
e st
ude
nts
?
24
Sol
ve e
ach
pro
por
tion
.
6.�2 5�
�� 4x 0�
167.
� 17 0��
�2 x1 �30
8.�2 50 �
��4 6x �
6
9.�5 4x �
��3 85 �
3.5
10.�
x� 3
1�
��7 2�
9.5
11.�
1 35 ��
�x� 5
3�
28
Fin
d t
he
mea
sure
s of
th
e si
des
of
each
tri
angl
e.
12.T
he
rati
o of
th
e m
easu
res
of t
he
side
s of
a t
rian
gle
is 3
:5:7
,an
d it
s pe
rim
eter
is
450
cen
tim
eter
s.90
cm
,150
cm
,210
cm
13.T
he r
atio
of
the
mea
sure
s of
the
sid
es o
f a
tria
ngle
is 5
:6:9
,and
its
peri
met
er is
220
met
ers.
55 m
,66
m,9
9 m
14.T
he
rati
o of
th
e m
easu
res
of t
he
side
s of
a t
rian
gle
is 4
:6:8
,an
d it
s pe
rim
eter
is
126
feet
.28
ft,
42 f
t,56
ft
15.T
he r
atio
of
the
mea
sure
s of
the
sid
es o
f a
tria
ngle
is
5:7:
8,an
d it
s pe
rim
eter
is
40 i
nche
s.10
in.,
14 in
.,16
in.
Answers (Lesson 7–1)
Chapter 7 A4 Glencoe Geometry
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Cha
pter
711
Gle
ncoe
Geo
met
ry
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Enri
chm
ent
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-1
Gro
wth
Ch
arts
It i
s sa
id t
hat
wh
en a
ch
ild
has
rea
ched
th
e ag
e of
2 y
ears
,he
is r
ough
ly h
alf
of h
isad
ult
hei
ght.
Th
e gr
owth
ch
art
belo
w s
how
s th
e gr
owth
acc
ordi
ng
to p
erce
nti
les
for
boys
.
1.U
se t
he
char
t to
det
erm
ine
the
appr
oxim
ate
hei
ght
for
a bo
y at
age
2 i
f h
e is
in
the
75th
to
95th
per
cen
tile
.
35–
37 in
ches
2.U
sin
g th
e ru
le t
hat
th
e h
eigh
t at
age
2 i
s ap
prox
imat
ely
hal
f of
his
adu
lt h
eigh
t,se
t u
p a
prop
orti
on t
o so
lve
for
the
adu
lt h
eigh
t of
th
e bo
y in
exe
rcis
e 1.
Sol
veyo
ur
prop
orti
on.
�3 x6 ��
�1 2� ;72
inch
es
3.U
se t
he
char
t to
app
roxi
mat
e th
e h
eigh
t at
age
18
for
a bo
y if
he
is i
n t
he
75th
to 9
5th
per
cen
tile
.How
doe
s th
is a
nsw
er c
ompa
re t
o th
e an
swer
to
prob
lem
1?
72–
74 in
ches
:th
e tw
o a
nsw
ers
are
very
clo
se
4.R
epea
t th
is p
roce
ss f
or a
boy
wh
o is
in
th
e 5t
h t
o 25
th p
erce
nti
le.
32–
34 in
ches
;64
inch
es;
65–
68 in
ches
5.Is
usi
ng
the
rule
th
at a
boy
is
hal
f of
his
adu
lt h
eigh
t at
age
2 y
ears
a g
ood
appr
oxim
atio
n?
Exp
lain
.
Yes,
it a
pp
ears
to
be
a g
oo
d a
pp
roxi
mat
ion
.
85 75 65 55 45 35
24
68
1012
1416
18
Ag
e (y
r)
Height (in.)
Perc
enti
le G
rou
p
5th
to
25t
h
25th
to
75t
h
75th
to
95t
h
A B
Lesson 7-1
1.M
OD
ELS
Lu
ke w
ants
to
mak
e a
scal
em
odel
of
a B
oein
g 74
7 je
tlin
er.H
e w
ants
ever
y fo
ot o
f h
is m
odel
to
repr
esen
t 50
feet
.Com
plet
e th
e fo
llow
ing
tabl
e.
(Sou
rce:
ww
w.b
oein
g.co
m)
2.R
ATI
ON
SS
ixte
en s
tude
nts
wen
t on
a
wee
k-lo
ng
hik
ing
trip
.Th
ey b
rou
ght
wit
h t
hem
320
spe
cial
ly b
aked
,pro
tein
-ri
ch,c
ooki
es.W
hat
is
the
rati
o of
coo
kies
to s
tude
nts
?20
:1
3.PH
OTO
GR
APH
ST
racy
is
4 fe
et
tall
an
d h
er f
ath
er i
s 6
feet
tal
l.In
a
phot
ogra
ph o
f th
e tw
o of
th
emst
andi
ng
side
by
side
,Tra
cy’s
im
age
is 2
in
ches
tal
l.
Alt
hou
gh t
hei
r im
ages
are
mu
ch s
mal
ler,
the
rati
o of
th
eir
hei
ghts
rem
ain
s th
esa
me.
How
tal
l is
Tra
cy’s
fat
her
’s i
mag
ein
th
e ph
oto?
3 in
.
4.C
AR
SA
car
com
pan
y bu
ilds
tw
ove
rsio
ns
of o
ne
of i
ts m
odel
s—a
seda
nan
d a
stat
ion
wag
on.T
he
rati
o of
sed
ans
to s
tati
on w
agon
s is
11
:2.A
fre
igh
ter
begi
ns
un
load
ing
the
cars
at
a do
ck.
Tom
cou
nts
18
stat
ion
wag
ons
and
then
over
hea
rs a
doc
k w
orke
r ca
ll o
ut,
“Oka
y,th
at’s
all
of
the
wag
ons
...b
rin
g ou
t th
e se
dan
s!”
How
man
y se
dan
s w
ere
onth
e sh
ip?
99
MA
PSF
or E
xerc
ises
5–7
,use
th
efo
llow
ing
info
rmat
ion
.C
arlo
s m
akes
a m
ap o
f h
is n
eigh
borh
ood
for
a pr
esen
tati
on.T
he
scal
e of
his
map
is
1 in
ch :
125
feet
.
5.H
ow m
any
feet
do
4 in
ches
rep
rese
nt
onth
e m
ap?
500
ft
6.C
arlo
s li
ves
250
feet
aw
ay f
rom
An
drew
.H
ow m
any
inch
es s
epar
ate
Car
los’
hom
efr
om A
ndr
ew’s
on
th
e m
ap?
2 in
.
7.D
uri
ng
a pr
acti
ce r
un
in
fro
nt
of h
ispa
ren
ts,C
arlo
s re
aliz
es t
hat
his
map
is
far
too
sm
all.
He
deci
des
to m
ake
his
map
5 t
imes
as
larg
e.W
hat
wou
ld
be t
he
scal
e of
th
e la
rger
map
?1
in.:
25 f
t
6 ft
4 ft
Cha
pter
710
Gle
ncoe
Geo
met
ry
Wor
d Pr
oble
m P
ract
ice
Pro
po
rtio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Act
ual
Mo
del
Par
tle
ng
th (
in.)
len
gth
(in
.)
Win
g S
pan
2,53
750
.74
Leng
th2,
782
55.6
4Ta
il H
eigh
t39
27.
84
Answers (Lesson 7–1)
Chapter 7 A5 Glencoe Geometry
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
An
swer
s
Cha
pter
713
Gle
ncoe
Geo
met
ry
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Less
on R
eadi
ng G
uide
Sim
ilar
Po
lyg
on
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-2
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 7
-2 i
n y
our
text
boo
k.
•D
escr
ibe
the
figu
res
that
hav
e si
mil
ar s
hap
es. S
amp
le a
nsw
er:
Lig
ht
and
dar
kfi
gu
res
are
arra
ng
ed in
alt
ern
atin
g p
atte
rns.
Fig
ure
s th
at h
ave
thei
r fe
etp
oin
tin
g t
ow
ard
th
e ce
nte
r o
f th
e ci
rcle
hav
e th
e sa
me
shap
e bu
t d
iffe
ren
tsi
zes.
•W
hat
hap
pen
s to
th
e fi
gure
s as
you
r ey
es m
ove
from
th
e ce
nte
r to
th
e ou
ter
edge
?S
amp
le a
nsw
er:T
he
fig
ure
s b
eco
me
smal
ler.
Rea
d t
he
Less
on
1.C
ompl
ete
each
sen
ten
ce.
a.T
wo
poly
gon
s th
at h
ave
exac
tly
the
sam
e sh
ape,
but
not
nec
essa
rily
th
e sa
me
size
,ar
e .
b.
Tw
o po
lygo
ns
are
con
gru
ent
if t
hey
hav
e ex
actl
y th
e sa
me
shap
e an
d th
e sa
me
.c.
Tw
o po
lygo
ns
are
sim
ilar
if
thei
r co
rres
pon
din
g an
gles
are
an
d th
eir
corr
espo
ndi
ng
side
s ar
e .
d.
Tw
o po
lygo
ns
are
con
gru
ent
if t
hei
r co
rres
pon
din
g an
gles
are
an
d th
eir
corr
espo
ndi
ng
side
s ar
e .
e.T
he
rati
o of
th
e le
ngt
hs
of c
orre
spon
din
g si
des
of t
wo
sim
ilar
fig
ure
s is
cal
led
the
.f.
Mu
ltip
lyin
g th
e co
ordi
nat
es o
f al
l po
ints
of
a fi
gure
in
th
e co
ordi
nat
e pl
ane
by a
sca
le
fact
or t
o ge
t a
sim
ilar
fig
ure
is
call
ed a
.
g.If
tw
o po
lygo
ns a
re s
imila
r w
ith
a sc
ale
fact
or o
f 1,
then
the
pol
ygon
s ar
e .
2.D
eter
min
e w
het
her
eac
h s
tate
men
t is
alw
ays,
som
etim
es,o
r n
ever
tru
e.a.
Tw
o si
mil
ar t
rian
gles
are
con
gru
ent.
som
etim
esb
.T
wo
equ
ilat
eral
tri
angl
es a
re c
ongr
uen
t.so
met
imes
c.A
n e
quil
ater
al t
rian
gle
is s
imil
ar t
o a
scal
ene
tria
ngl
e.n
ever
d.
Tw
o re
ctan
gles
are
sim
ilar
.so
met
imes
e.T
wo
isos
cele
s ri
ght
tria
ngl
es a
re c
ongr
uen
t.so
met
imes
f.T
wo
isos
cele
s ri
ght
tria
ngl
es a
re s
imil
ar.
alw
ays
g.A
squ
are
is s
imil
ar t
o an
equ
ilat
eral
tri
angl
e.n
ever
h.
Tw
o ac
ute
tri
angl
es a
re s
imil
ar.
som
etim
esi.
Tw
o re
ctan
gles
in
wh
ich
th
e le
ngt
h i
s tw
ice
the
wid
th a
re s
imil
ar.
alw
ays
j.T
wo
con
gru
ent
poly
gon
s ar
e si
mil
ar.
alw
ays
Rem
emb
er W
hat
Yo
u L
earn
ed3.
A g
ood
way
to
rem
embe
r a
new
mat
hem
atic
al v
ocab
ula
ry t
erm
is
to r
elat
e it
to
wor
dsu
sed
in e
very
day
life
.Th
e w
ord
scal
eh
as m
any
mea
nin
gs i
n E
ngl
ish
.Giv
e th
ree
phra
ses
that
in
clu
de t
he
wor
d sc
ale
in a
way
th
at i
s re
late
d to
pro
port
ion
s.S
amp
le a
nsw
er:
scal
e d
raw
ing
,sca
le m
od
el,s
cale
of
mile
s (o
n a
map
)
con
gru
ent
dila
tio
n
scal
e fa
cto
r
con
gru
ent
con
gru
ent
pro
po
rtio
nal
con
gru
ent
sizesi
mila
r
Lesson 7-2
Cha
pter
712
Gle
ncoe
Geo
met
ry
Gra
phin
g Ca
lcul
ator
Act
ivit
yS
olv
ing
Pro
po
rtio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
You
can
use
a c
alcu
lato
r to
sol
ve p
ropo
rtio
ns.
Sol
ve t
he
pro
por
tion
by
usi
ng
cros
s p
rod
uct
s.
�5 15 6. .6 9��
�45x.8 �
Mu
ltip
ly 1
6.9
by 4
5.8.
Div
ide
the
prod
uct
by
55.6
.
En
ter:
16.9
45
.8
55.6
13
.92
122
30
2
Th
e so
luti
on is
app
roxi
mat
ely
13.9
21.
Sol
ve e
ach
pro
por
tion
by
usi
ng
cros
s p
rod
uct
s.R
oun
d y
our
answ
ers
to t
he
nea
rest
hu
nd
red
th.
1.�1 33 9. .9 8�
��1
0 x.5 �2.
�2 35 7. .9 7��
�24x.3 �
3.�1 59 4. .6 3�
��27
x.7 �
x�
30.0
6x
�35
.37
x�
76.7
4
4.�6 46 3. .8 4�
�� 16
x .9�5.
�7 35 7. .4 2��
� 32x .4�
6.� 46
x .2��
�2 39 6. .7 4�
x �
26.0
1x
�65
.67
x �
37.7
0
7.� 14
x .9��
�1 26 4. .8 6�8.
�35x.8 �
�
�3 22 7. .9 8�9.
�46x.9 �
��1 95 9. .7 9�
x�
10.1
8x
�30
.25
x�
298.
43
10.
�3 24 1. .9 1��
� 36x .6�
11.
� 99x .8�
��3 42 5. .2 3�
12.
�68x.9 �
��4 84 6. .3 4�
x�
60.5
4x
�70
.94
x�
134.
38
EN
TER
��
Exam
ple
Answers (Lessons 7–1 and 7–2)
Chapter 7 A6 Glencoe Geometry
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Cha
pter
715
Gle
ncoe
Geo
met
ry
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nued
)
Sim
ilar
Po
lyg
on
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-2
Scal
e Fa
cto
rsW
hen
tw
o po
lygo
ns
are
sim
ilar
,th
e ra
tio
of t
he
len
gth
s of
cor
resp
ondi
ng
side
s is
cal
led
the
scal
e fa
ctor
.At
the
righ
t,�
AB
C�
�X
YZ
.Th
e sc
ale
fact
or o
f �
AB
Cto
�X
YZ
is 2
an
d th
e sc
ale
fact
or o
f
�X
YZ
to �
AB
Cis
�1 2� .3
cm
6 cm
8 cm
10 c
m5
cm4
cm ZY
XCA
B
Th
e tw
o p
olyg
ons
are
sim
ilar
.Fin
d x
and
y.
Use
th
e co
ngr
uen
t an
gles
to
wri
te t
he
corr
espo
ndi
ng
vert
ices
in
ord
er.
�R
ST
��
MN
PW
rite
pro
port
ion
s to
fin
d x
and
y.
�3 12 6��
� 1x 3��3 y8 �
��3 12 6�
16x
�32
(13)
32y
�38
(16)
x�
26y
�19
x
y38
3216
13T
S
RP
N
M
�A
BC
��
CD
E.F
ind
th
e sc
ale
fact
or a
nd
fin
d t
he
len
gth
s of
C �D�
and
D�E�
.
AC
�3
�0
�3
and
CE
�9
�3
�6.
Th
esc
ale
fact
or o
f �
CD
Eto
�A
BC
is 6
:3 o
r 2:
1.U
sin
g th
e D
ista
nce
For
mu
la,
AB
��
1 �
9�
��
10�an
d B
C�
�4
�9
��
�13�
.Th
e le
ngt
hs
of t
he
side
s of
�C
DE
are
twic
e th
ose
of �
AB
C,
so D
C�
2(B
A)
or 2
�10�
and
DE
�2(
BC
) or
2�
13�.
x
y
A( 0
, 0)
B( 1
, 3) C( 3
, 0)
E( 9
, 0)
D
Eac
h p
air
of p
olyg
ons
is s
imil
ar.F
ind
xan
d y
.
1.2.
x�
6;y
�15
x�
2.25
;y
�5
3.4.
x�
27;
y�
15x
�24
;y
�27
5.In
Exa
mpl
e 2
abov
e,po
int
Dh
as c
oord
inat
es (
5,6)
.Use
th
e D
ista
nce
For
mu
la t
o ve
rify
the
len
gth
s of
C �D�
and
D�E�
.
CD
�2�
10�,D
E�
2�13�
40
36x
30
18y
12
y �
1
18
24
x18
10y
4.5
x2.
5 5
9
12y8 10
x
Exam
ple
1Ex
amp
le 2
Exer
cise
s
Lesson 7-2
Cha
pter
714
Gle
ncoe
Geo
met
ry
Stud
y G
uide
and
Inte
rven
tion
Sim
ilar
Po
lyg
on
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Iden
tify
Sim
ilar
Fig
ure
s
Det
erm
ine
wh
eth
er t
he
tria
ngl
es
are
sim
ilar
.T
wo
poly
gon
s ar
e si
mil
ar i
f an
d on
ly i
f th
eir
corr
espo
ndi
ng
angl
es a
re c
ongr
uen
t an
d th
eir
corr
espo
ndi
ng
side
s ar
e pr
opor
tion
al.
�C
��
Zbe
cau
se t
hey
are
rig
ht
angl
es,a
nd
�B
��
X.
By
the
Th
ird
An
gle
Th
eore
m,�
A�
�Y
.
For
th
e si
des,
�B XC Z�
��2 20 3�
,�B X
A Y��
��2 20 3�
,an
d �A Y
C Z��
�2 20 3�.
Th
e si
de l
engt
hs
are
prop
orti
onal
.So
�B
CA
��
XZ
Y.
Is p
olyg
on W
XY
Z�
pol
ygon
PQ
RS
?
For
th
e si
des,
�W PQX �
��1 82 �
��3 2� ,
� QXY R�
��1 18 2�
��3 2� ,
� RYZ S�
��1 15 0�
��3 2� ,
and
�Z SW P��
�9 6��
�3 2� .S
o co
rres
pon
din
g si
des
are
prop
orti
onal
.
Als
o,�
W�
�P
,�X
��
Q,�
Y�
�R
,an
d �
Z�
�S
,so
corr
espo
ndi
ng
angl
es a
re c
ongr
uen
t.W
e ca
n c
oncl
ude
th
at
poly
gon
WX
YZ
�po
lygo
n P
QR
S.
Det
erm
ine
wh
eth
er e
ach
pai
r of
fig
ure
s is
sim
ilar
.If
they
are
sim
ilar
,giv
e th
era
tio
of c
orre
spon
din
g si
des
.
1.2.
yes;
�5 8�n
o
3.4.
yes;
�1 2�ye
s;�5 4�
10y
8y
37�
37�
116�
27�
5 x
4x15
z12
z
2211
1610 equi
late
ral t
riang
les
15
9
12
18XW
ZY
10
6
8
12
QP S
R
20�
2�� 23
�2�
2023
2320
20�
�223
��2
45�
45�
CA
XZ
BY
Exam
ple
1
Exam
ple
2
Exer
cise
s
Answers (Lesson 7–2)
Chapter 7 A7 Glencoe Geometry
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
An
swer
s
Cha
pter
717
Gle
ncoe
Geo
met
ry
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Prac
tice
Sim
ilar
Po
lyg
on
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-2
Det
erm
ine
wh
eth
er e
ach
pai
r of
fig
ure
s is
sim
ilar
.Ju
stif
y yo
ur
answ
er.
1.2.
JKL
M�
QR
SP
;�
AB
C�
�U
VT
;�
A�
�U
,�
J�
�Q
,�K
��
R,
�B
��
V,a
nd
�C
��
Tby
th
e �
L�
�S
,�M
��
P,a
nd
T
hir
d A
ng
le T
heo
rem
an
d
� QJKR�
�� RK
SL ��
�L SM P��
� PMQJ �
��5 3�
or
1.67
�A UB V�
��B V
C T��
�C TUA �
��2 3� .
Eac
h p
air
of p
olyg
ons
is s
imil
ar.W
rite
a s
imil
arit
y st
atem
ent,
and
fin
d x
,th
em
easu
re(s
) of
th
e in
dic
ated
sid
e(s)
,an
d t
he
scal
e fa
ctor
.
3.L �
M�an
d M�
N�4.
D�E�
and
D�F�
AB
CD
�L
MN
P;
�A
BC
��
DE
F;
�3 2� ;10
�1 2� ;7�
1 2� ;�4 3�
7;4;
8;�3 2�
5.C
OO
RD
INA
TE G
EOM
ETRY
Tri
angl
e A
BC
has
ver
tice
s A
(0,0
),B
(�4,
0),a
nd
C(�
2,4)
.T
he
coor
din
ates
of
each
ver
tex
are
mu
ltip
lied
by
3 to
cre
ate
�A
EF
.Sh
ow t
hat
�A
EF
issi
mil
ar t
o �
AB
C.
AB
�4,
BC
�C
A�
2�5�
and
AE
�12
,EF
�FA
�6�
5�.�A A
B E��
�B EC F�
��C FA
A ��
�1 3� ;�
A�
�A
and
sin
ce B�
C�|| E�
F�,�
B�
�E
and
�C
��
F.S
ince
th
e co
rres
po
nd
ing
an
gle
s ar
e co
ng
ruen
t an
d t
he
corr
esp
on
din
g s
ides
are
pro
po
rtio
nal
,�A
BC
��
AE
F.
6.IN
TER
IOR
DES
IGN
Gra
ham
use
d th
e sc
ale
draw
ing
of h
is l
ivin
g ro
om t
o de
cide
wh
ere
to p
lace
fu
rnit
ure
.Fin
d th
e di
men
sion
s of
th
eli
vin
g ro
om i
f th
e sc
ale
in t
he
draw
ing
is 1
in
ch �
4.5
feet
.18
ft
by 1
1 ft
3 in
.4
in.
21 – 2 in.
612
40�
40�
x �
1
x �
3A
F
E
D
BC
14
10
x �
6
x �
9
CN
MD
AB
LP
2412
1416
2118
VU
AC
BT
2512
9
14.4
1524
20
15
JM
QRS
PK
L
Lesson 7-2
Cha
pter
716
Gle
ncoe
Geo
met
ry
Skill
s Pr
acti
ceS
imila
r P
oly
go
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Det
erm
ine
wh
eth
er e
ach
pai
r of
fig
ure
s is
sim
ilar
.Ju
stif
y yo
ur
answ
er.
1.2.
�A
BC
��
DE
F;
�A
��
D,
rho
mbu
s P
QR
S�
rho
mbu
s W
XY
Z;
�C
��
F,a
nd
�B
��
E�
P�
�W
,�Q
��
X,�
R�
�Y
,b
ecau
se if
tw
o a
ng
les
of
on
e �
S�
�Z
;tr
ian
gle
are
co
ng
ruen
t to
tw
o
� WPQ X�
��Q X
YR ��
�R YS Z�
�� ZS WP �
�� 73 .5�
�0.
4an
gle
s o
f a
seco
nd
tri
ang
le,t
hen
th
e th
ird
an
gle
s ar
e co
ng
ruen
t;
�A DB E�
��B E
C F��
�C FDA �
��3 2� .
Eac
h p
air
of p
olyg
ons
is s
imil
ar.W
rite
a s
imil
arit
y st
atem
ent,
and
fin
d x
,th
em
easu
re(s
) of
th
e in
dic
ated
sid
e(s)
,an
d t
he
scal
e fa
ctor
.
3.G �
H�4.
S�T�
and
S�U�
AB
CD
�E
FG
H;
�W
XY
��
ST
U(o
r �
SU
T)
6�1 2� ;
6�1 2� ;
27;
12;
12;
�1 3�
5.W�
T�6.
T�S�
and
S�P�
PQ
RS
�U
VW
T;
�L
MN
��
TS
P;
5;6;
�3 2�13
;12
;15
;�2 3�
10
8
x �
2
x �
1
SP
MN
L
T
9
10 3
x �
1
5
P
S
RU
V
WT
Q
x �
5
x �
5
9
3
44
S
W
XY
T U2614
1213
BC
DA
1376
x G
EH
F
7.5
7.5
7.5
7.5
ZY
XW
3
3
33
SR
QP
10.5
69
59�
35�
AC
B
7
46
59�
35�
DF
E
Answers (Lesson 7–2)
Chapter 7 A8 Glencoe Geometry
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Cha
pter
719
Gle
ncoe
Geo
met
ry
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Enri
chm
ent
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-2
Co
nst
ruct
ing
Sim
ilar
Po
lyg
on
sH
ere
are
fou
r st
eps
for
con
stru
ctin
g a
poly
gon
th
at i
s si
mil
ar t
o an
d w
ith
si
des
twic
e as
lon
g as
th
ose
of a
n e
xist
ing
poly
gon
.
Ste
p 1
Ch
oose
an
y po
int
eith
er i
nsi
de o
r ou
tsid
e th
e po
lygo
n a
nd
labe
l it
O.
Ste
p 2
Dra
w r
ays
from
Oth
rou
gh e
ach
ver
tex
of t
he
poly
gon
.S
tep
3F
or v
erte
x V
,set
th
e co
mpa
ss t
o le
ngt
h O
V.T
hen
loc
ate
a n
ew p
oin
tV
�on
ray
OV
such
th
at V
V�
�O
V.T
hu
s,O
V�
�2(
OV
).S
tep
4R
epea
t S
tep
3 fo
r ea
ch v
erte
x.C
onn
ect
poin
ts V
�,W
�,X
�an
d Y
�to
form
th
e n
ew p
olyg
on.
Tw
o co
nst
ruct
ion
s of
pol
ygon
s si
mil
ar t
o an
d w
ith
sid
es t
wic
e th
ose
of V
WX
Yar
e sh
own
bel
ow.N
otic
e th
at t
he
plac
emen
t of
poi
nt
Odo
es n
ot a
ffec
t th
e si
zeor
sh
ape
of V
�W�X
�Y�,
only
its
loc
atio
n.
Tra
ce e
ach
pol
ygon
.Th
en c
onst
ruct
a s
imil
ar p
olyg
on w
ith
sid
es t
wic
e as
lon
g as
thos
e of
th
e gi
ven
pol
ygon
.S
ee s
tud
ents
’co
nst
ruct
ion
s.
1.2.
DE
F
GC
A
B
VW
YX
VW
YX
V�
W�
X�
Y�
O
VW
YX
V�
W�
X�
Y�
O
3.E
xpla
in h
ow t
o co
nst
ruct
a s
imil
arpo
lygo
n w
ith
side
s th
ree
tim
es t
he l
engt
hof
th
ose
of p
olyg
on H
IJK
L.T
hen
do
the
con
stru
ctio
n.
See
stu
den
ts’w
ork
.
4.E
xpla
in h
ow t
o co
nst
ruct
a s
imil
ar
poly
gon
1�1 2�
tim
es t
he
len
gth
of
thos
e of
poly
gon
MN
PQ
RS
.Th
en d
o th
eco
nst
ruct
ion
.S
ee s
tud
ents
’wo
rk.
M
S
R
N
Q
P
HI
LK
J
Lesson 7-2
Cha
pter
718
Gle
ncoe
Geo
met
ry
Wor
d Pr
oble
m P
ract
ice
Sim
ilar
Po
lyg
on
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.PA
NEL
SW
hen
clo
sed,
an e
nte
rtai
nm
ent
cen
ter
is m
ade
of f
our
squ
are
pan
els.
Th
e th
ree
smal
ler
pan
els
are
con
gru
ent
squ
ares
.
Wh
at i
s th
e sc
ale
fact
or o
f th
e la
rger
squ
are
to o
ne
of t
he
smal
ler
squ
ares
?3
2.D
OW
NSP
OU
TSD
uri
ng
a st
orm
,on
e of
th
e do
wn
spou
ts o
n M
r.H
erre
ra’s
hou
se w
as b
roke
n a
nd
nee
ded
to b
ere
plac
ed.U
nfo
rtu
nat
ely,
the
dow
nsp
out
was
too
dam
aged
to
mea
sure
its
len
gth
and
it w
as t
oo d
iffi
cult
to
mea
sure
th
eh
eigh
t of
th
e gu
tter
.Lu
ckil
y,M
r.H
erre
rah
ad a
sca
le m
odel
of
his
hou
se.I
f th
e do
wn
spou
t in
th
e m
odel
was
1�1 2�
feet
lo
ng
and
the
scal
e fa
ctor
was
20,
how
lon
g w
as t
he
actu
al d
own
spou
t?30
ft
3.O
RIG
AM
IB
axte
r u
ses
an 8
-in
ch
squ
are
piec
e of
ori
gam
i pa
per
to m
ake
an o
riga
mi
mod
el o
f a
chic
ken
.Wh
enfi
nis
hed
,th
e ch
icke
n s
tan
ds 4
in
ches
hig
h.B
axte
r w
ants
to
mak
e an
oth
eror
igam
i ch
icke
n,o
nly
th
is t
ime
he
wan
ts t
o m
ake
it 1
2 in
ches
hig
h i
nst
ead.
Wh
at s
ize
piec
e of
pap
er s
hou
ld h
e u
seto
do
this
?2
ft s
qu
are
4.EN
LAR
GIN
GC
amil
le w
ants
to
mak
e a
patt
ern
for
a f
our-
poin
ted
star
wit
hdi
men
sion
s tw
ice
as l
ong
as t
he
one
show
n.H
elp
her
by
draw
ing
a st
ar w
ith
dim
ensi
ons
twic
e as
lon
g on
th
e gr
idbe
low
.
BIO
LOG
YF
or E
xerc
ises
5–7
,use
th
efo
llow
ing
info
rmat
ion
.A
par
amec
ium
is
a sm
all
sin
gle-
cell
orga
nis
m.T
he
para
mec
ium
mag
nif
ied
belo
wis
act
ual
ly o
ne
ten
th o
f a
mil
lim
eter
lon
g.
5.If
you
wan
t to
mak
e a
phot
ogra
ph o
f th
eor
igin
al p
aram
eciu
m s
o th
at i
ts i
mag
e is
1 ce
nti
met
er l
ong,
by w
hat
sca
le f
acto
rsh
ould
you
mag
nif
y it
?10
0
6.If
you
wan
t to
mak
e a
phot
ogra
ph o
f th
eor
igin
al p
aram
eciu
m s
o th
at i
ts i
mag
e is
15 c
enti
met
ers
lon
g,by
wh
at s
cale
fac
tor
shou
ld y
ou m
agn
ify
it?
1500
7.B
y ap
prox
imat
ely
wh
at s
cale
fac
tor
has
the
para
mec
ium
bee
n e
nla
rged
to
mak
eth
e im
age
show
n?
400
Answers (Lesson 7–2)
Chapter 7 A9 Glencoe Geometry
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
An
swer
s
Cha
pter
721
Gle
ncoe
Geo
met
ry
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
Sim
ilar T
rian
gle
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-3
Iden
tify
Sim
ilar
Tria
ng
les
Her
e ar
e th
ree
way
s to
sh
ow t
hat
tw
o tr
ian
gles
are
sim
ilar
.
AA
Sim
ilari
tyTw
o an
gles
of
one
tria
ngle
are
con
grue
nt t
o tw
o an
gles
of
anot
her
tria
ngle
.
SS
S S
imila
rity
The
mea
sure
s of
the
cor
resp
ondi
ng s
ides
of
two
tria
ngle
s ar
e pr
opor
tiona
l.
SA
S S
imila
rity
The
mea
sure
s of
tw
o si
des
of o
ne t
riang
le a
re p
ropo
rtio
nal t
o th
e m
easu
res
of
two
corr
espo
ndin
g si
des
of a
noth
er t
riang
le,
and
the
incl
uded
ang
les
are
cong
ruen
t.
Det
erm
ine
wh
eth
er t
he
tria
ngl
es a
re s
imil
ar.
� DAC F�
��6 9�
��2 3�
�B EC F�
�� 18 2�
��2 3�
� DAB E�
��1 10 5�
��2 3�
�A
BC
��
DE
Fby
SS
S S
imil
arit
y.
15
129
DE
F
10
86
AB
C
Det
erm
ine
wh
eth
er t
he
tria
ngl
es a
re s
imil
ar.
�3 4��
�6 8� ,so
�M QRN �
��N R
SP �.
m�
N�
m�
R,s
o �
N�
�R
.�
NM
P�
�R
QS
by S
AS
Sim
ilar
ity.
8
4 70�Q
RS
6
3 70�
M
NP
Det
erm
ine
wh
eth
er e
ach
pai
r of
tri
angl
es i
s si
mil
ar.J
ust
ify
you
r an
swer
.
1.2.
yes;
AA
Sim
ilari
tyn
o;
�3 26 4��
�2 10 8�
3.4.
yes;
AA
Sim
ilari
tyye
s;S
AS
Sim
ilari
ty
5.6.
yes;
SA
S S
imila
rity
yes;
SS
S S
imila
rity
32
20
1540
2524
3926
1624
18
8 65�
9
4 65�
36
2018
24
Exam
ple
1Ex
amp
le 2
Exer
cise
s
Lesson 7-3
Cha
pter
720
Gle
ncoe
Geo
met
ry
Less
on R
eadi
ng G
uide
Sim
ilar T
rian
gle
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 7
-3 i
n y
our
text
boo
k.
•W
hat
doe
s it
mea
n t
o sa
y th
at t
rian
gula
r sh
apes
res
ult
in
rig
id c
onst
ruct
ion
?S
amp
le a
nsw
er:
A t
rian
gu
lar
stru
ctu
re w
ill n
ot
chan
ge
its
shap
e o
rsi
ze if
yo
u p
ush
on
its
sid
es w
ith
ou
t b
reak
ing
or
ben
din
g t
hem
.•
Wh
at w
ould
hap
pen
if
the
shap
es u
sed
in t
he
con
stru
ctio
n w
ere
quad
rila
tera
ls?
Sam
ple
an
swer
:Th
e st
ruct
ure
mig
ht
colla
pse
,bec
ause
qu
adri
late
rals
are
no
t ri
gid
.
Rea
d t
he
Less
on
1.S
tate
wh
eth
er e
ach
con
diti
on g
uar
ante
es t
hat
tw
o tr
ian
gles
are
con
gru
ent
or s
imil
ar.
If t
he
con
diti
on g
uar
ante
es t
hat
th
e tr
ian
gles
are
bot
h s
imil
ar a
nd
con
gru
ent,
wri
teco
ngr
uen
t.If
th
ere
is n
ot e
nou
gh i
nfo
rmat
ion
to
guar
ante
e th
at t
he
tria
ngl
es w
ill
beco
ngr
uen
t or
sim
ilar
,wri
te n
eith
er.
a.T
wo
side
s an
d th
e in
clu
ded
angl
e of
on
e tr
ian
gle
are
con
gru
ent
to t
wo
side
s an
d th
ein
clu
ded
angl
e of
th
e ot
her
tri
angl
e.co
ng
ruen
tb
.T
he
mea
sure
s of
all
th
ree
pair
s of
cor
resp
ondi
ng
side
s ar
e pr
opor
tion
al.
sim
ilar
c.T
wo
angl
es o
f on
e tr
ian
gle
are
con
gru
ent
to t
wo
angl
es o
f th
e ot
her
tri
angl
e.si
mila
rd
.T
wo
angl
es a
nd
a n
onin
clu
ded
side
of
one
tria
ngl
e ar
e co
ngr
uen
t to
tw
o an
gles
an
dth
e co
rres
pon
din
g n
onin
clu
ded
side
of
the
oth
er t
rian
gle.
con
gru
ent
e.T
he
mea
sure
s of
tw
o si
des
of a
tri
angl
e ar
e pr
opor
tion
al t
o th
e m
easu
res
of t
wo
corr
espo
ndi
ng
side
s of
an
oth
er t
rian
gle,
and
the
incl
ude
d an
gles
are
con
gru
ent.
sim
ilar
f.T
he
thre
e si
des
of o
ne
tria
ngl
e ar
e co
ngr
uen
t to
th
e th
ree
side
s of
th
e ot
her
tri
angl
e.co
ng
ruen
tg.
The
thr
ee a
ngle
s of
one
tri
angl
e ar
e co
ngru
ent
to t
he t
hree
ang
les
of t
he o
ther
tri
angl
e.si
mila
rh
.O
ne
acu
te a
ngl
e of
a r
igh
t tr
ian
gle
is c
ongr
uen
t to
on
e ac
ute
an
gle
of a
not
her
rig
ht
tria
ngl
e.si
mila
ri.
Th
e m
easu
res
of t
wo
side
s of
a t
rian
gle
are
prop
orti
onal
to
the
mea
sure
s of
tw
o si
des
of a
not
her
tri
angl
e.n
eith
er2.
Iden
tify
eac
h of
the
fol
low
ing
as a
n ex
ampl
e of
a r
efle
xive
,sym
met
ric,
or t
rans
itiv
epr
oper
ty.
a.If
�R
ST
��
UV
W,t
hen
�U
VW
��
RS
T.
sym
met
ric
b.
If �
RS
T�
�U
VW
and
�U
VW
��
OP
Q,t
hen
�R
ST
��
OP
Q.
tran
siti
vec.
�R
ST
��
RS
Tre
flex
ive
Rem
emb
er W
hat
Yo
u L
earn
ed3.
A g
ood
way
to
rem
embe
r so
met
hin
g is
to
expl
ain
it
to s
omeo
ne
else
.Su
ppos
e on
e of
you
rcl
assm
ates
is
hav
ing
trou
ble
un
ders
tan
din
g th
e di
ffer
ence
bet
wee
n S
AS
for
con
gru
ent
tria
ngl
es a
nd
SA
S f
or s
imil
ar t
rian
gles
.How
can
you
exp
lain
th
e di
ffer
ence
to
him
?S
amp
le a
nsw
er:
In S
AS
fo
r co
ng
ruen
ce,c
orr
esp
on
din
g s
ides
are
con
gru
ent,
wh
ile in
SA
S f
or
sim
ilari
ty,c
orr
esp
on
din
g s
ides
are
pro
po
rtio
nal
.(In
bo
th,t
he
incl
ud
ed a
ng
les
are
con
gru
ent.
)
Answers (Lesson 7–3)
Chapter 7 A10 Glencoe Geometry
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Cha
pter
723
Gle
ncoe
Geo
met
ry
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Skill
s Pr
acti
ceS
imila
r Tri
ang
les
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-3
Det
erm
ine
wh
eth
er e
ach
pai
r of
tri
angl
es i
s si
mil
ar.J
ust
ify
you
r an
swer
.
1.2.
No
;th
e si
des
are
no
t p
rop
ort
ion
al.
yes;
�A
BC
��
PQ
R(o
r �
QP
R);
SS
S S
imila
rity
3.4.
yes;
�S
TU
��
JPM
;ye
s;�
SK
M�
�R
TQ
;S
AS
Sim
ilari
tyA
A S
imila
rity
ALG
EBR
AId
enti
fy t
he
sim
ilar
tri
angl
es,a
nd
fin
d x
and
th
e m
easu
res
of t
he
ind
icat
ed s
ides
.
5.A �
C�an
d E�
D�6.
J�L�an
d L�
M�
�A
BC
��
DB
E;
15;
16;
20�
JKL
��
MN
L;
10;
28;
7
7.E�
H�an
d E�
F�8.
V�T�
and
S�T�
�D
EF
��
GE
H;
4;9;
18�
RS
T�
�U
VT
;7.
5;1.
5;5
6
14
S
U
V
RT
x �
4 x �
612
9
6
9
D
E
FH G
x �
5
16
4MN
L
J
K
x �
18
x �
3
1512
D
EC
BAx
� 1
x �
5
30�
60�
RQM
S
K
T
2170
�
15
MJ
P
1470
�10
U
S
T
12
128
9
96
CP
QR
A
B
2014
1312
219 S
WX
Y
R
T
Lesson 7-3
Cha
pter
722
Gle
ncoe
Geo
met
ry
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nued
)
Sim
ilar T
rian
gle
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Use
Sim
ilar
Tria
ng
les
Sim
ilar
tri
angl
es c
an b
e u
sed
to f
ind
mea
sure
men
ts.
�A
BC
��
DE
F.
Fin
d x
and
y.
� DAC F�
��B E
C F�� DA
B E��
�B EC F�
��1 98 �
� 1y 8��
�1 98 �
18x
�9(
18�
3�)9y
�32
4x
�9 �
3�y
�36
18�
3��
x
18�
�3
B CA
1818
9y
x
E FD
A p
erso
n 6
fee
t ta
ll c
asts
a 1.
5-fo
ot-l
ong
shad
ow a
t th
e sa
me
tim
eth
at a
fla
gpol
e ca
sts
a 7-
foot
-lon
gsh
adow
.How
tal
l is
th
e fl
agp
ole?
Th
e su
n’s
ray
s fo
rm s
imil
ar t
rian
gles
.U
sin
g x
for
the
hei
ght
of t
he
pole
,�6 x�
��1 7.5 �
,so
1.5
x�
42 a
nd
x�
28.
Th
e fl
agpo
le i
s 28
fee
t ta
ll.
7 ft
6 ft
?
1.5
ft
Eac
h p
air
of t
rian
gles
is
sim
ilar
.Fin
d x
and
y.
1.2.
x�
26;
y�
17.5
x�
24;
y�
30
3.4.
x�
12;
y�
24�
2�x
�19
.3;
y�
46
5.6.
x�
18;
y�
10.8
x�
10�2 3� ;
y�
16�1 2�
7.T
he
hei
ghts
of
two
vert
ical
pos
ts a
re 2
met
ers
and
0.45
met
er.W
hen
th
e sh
orte
r po
stca
sts
a sh
adow
th
at i
s 0.
85 m
eter
lon
g,w
hat
is
the
len
gth
of
the
lon
ger
post
’s s
had
ow
to t
he
nea
rest
hu
ndr
edth
?3.
78 m
y
x32
10
2230
yx
9
87.2
16
yx
6038
.623
3024
36�
�2y
x
3636
20 13
26y
x �
235
13
1020
y
x
Exam
ple
1Ex
amp
le 2
Exer
cise
s
Answers (Lesson 7–3)
Chapter 7 A11 Glencoe Geometry
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
An
swer
s
Cha
pter
725
Gle
ncoe
Geo
met
ry
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Wor
d Pr
oble
m P
ract
ice
Sim
ilar T
rian
gle
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-3
Lesson 7-3
1.M
INIA
TUR
ESM
arla
lik
es h
er c
hai
r so
mu
ch t
hat
sh
e de
cide
s to
mak
e a
min
iatu
re r
epli
ca o
f it
for
her
pet
ham
ster
.Fin
d th
e va
lue
of x
.
3.75
in.
2.M
OD
ELS
Jim
has
a s
cale
mod
el o
f h
issa
ilbo
at.T
he
figu
re s
how
s dr
awin
gs o
fth
e or
igin
al s
ailb
oat
and
the
mod
el.
Fin
d x.
160
in.
3.G
EOM
ETRY
Geo
rgia
dra
ws
a re
gula
rpe
nta
gon
an
d st
arts
con
nec
tin
g it
sve
rtic
es t
o m
ake
a 5-
poin
ted
star
.Aft
erdr
awin
g th
ree
of t
he
lin
es i
n t
he
star
,sh
ebe
com
es c
uri
ous
abou
t tw
o tr
ian
gles
that
app
ear
in t
he
figu
re,�
AB
Can
d�
BC
E.T
hey
loo
k si
mil
ar t
o h
er.P
rove
that
th
is i
s th
e ca
se.
Sam
ple
an
swer
:m
�A
DB
�10
8,so
m�
DB
A�
36 (
bas
e o
f is
o-
scel
es �
AB
D).
Th
us,
m�
AB
C�
72°.
Sim
ilarl
y,m
�D
CB
�36
°an
dm
�A
CB
�72
°.S
o,m
�B
EC
�72
°an
d m
�B
AC
�36
°.T
her
efo
re,
�A
BC
and
�B
CE
are
sim
ilar.
4.SH
AD
OW
SA
rad
io t
ower
cas
ts a
shad
ow 8
fee
t lo
ng
at t
he
sam
e ti
me
that
a v
erti
cal
yard
stic
k ca
sts
a sh
adow
hal
f an
in
ch l
ong.
How
tal
l is
th
e ra
dio
tow
er?
576
ft
MO
UN
TAIN
PEA
KS
For
Exe
rcis
es 5
an
d6,
use
th
e fo
llow
ing
info
rmat
ion
.G
avin
an
d B
rian
na
wan
t to
kn
ow h
ow f
ar a
mou
nta
in p
eak
is f
rom
th
eir
hou
ses.
Th
eym
easu
re t
he
angl
es b
etw
een
th
e li
ne
of s
ite
to t
he
peak
an
d to
eac
h o
ther
’s h
ouse
s an
dca
refu
lly
mak
e th
e dr
awin
g sh
own
.
Th
e ac
tual
dis
tan
ce b
etw
een
Gav
in a
nd
Bri
ann
a’s
hou
se i
s 1�
1 2�m
iles
.
5.W
hat
is
the
actu
al d
ista
nce
of
the
mou
nta
in p
eak
from
Gav
in’s
hou
se?
Rou
nd
you
r an
swer
to
the
nea
rest
te
nth
of
a m
ile.
12.2
mi
6.W
hat
is
the
actu
al d
ista
nce
of
the
mou
nta
in p
eak
from
Bri
ann
a’s
hou
se?
Rou
nd
you
r an
swer
to
the
nea
rest
te
nth
of
a m
ile.
12.3
mi
Gavi
n
Bria
nna
Peak
2 in
.
2.01
5 in
.0.
246
in.
90˚
83˚
A
B
D
E
C
52˚
203
in.
10.1
5 in
.8
in.
52˚
x in
.
14”
3.5
”
15”
x
Cha
pter
724
Gle
ncoe
Geo
met
ry
Prac
tice
Sim
ilar T
rian
gle
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Det
erm
ine
wh
eth
er e
ach
pai
r of
tri
angl
es i
s si
mil
ar.J
ust
ify
you
r an
swer
.
1.2.
yes;
�JA
K�
�W
SY
;N
o;
the
sid
es a
re n
ot
pro
po
rtio
nal
.S
AS
Sim
ilari
ty
ALG
EBR
AId
enti
fy t
he
sim
ilar
tri
angl
es,a
nd
fin
d x
and
th
e m
easu
res
of t
he
ind
icat
ed s
ides
.
3.L �
M�an
d Q�
P�4.
N�L�
and
M�L�
�L
MN
��
PQ
N;
9;12
;8
�JL
N�
�K
LM
;2;
21;
14
Use
th
e gi
ven
in
form
atio
n t
o fi
nd
eac
h m
easu
re.
5.If
T�S�
|| Q�R�
,TS
�6,
PS
�x
�7,
6.If
E�F�
|| H�I�,
EF
�3,
EG
�x
�1,
QR
�8,
and
SR
�x
�1,
HI
�4,
and
HG
�x
�3,
fin
d P
San
d P
R.
fin
d E
Gan
d H
G.
PS
�12
;P
R�
16E
G�
6;H
G�
8
IND
IREC
T M
EASU
REM
ENT
For
Exe
rcis
es 7
an
d 8
,use
th
e fo
llow
ing
info
rmat
ion
.A
lig
hth
ouse
cas
ts a
128
-foo
t sh
adow
.A n
earb
y la
mpp
ost
that
mea
sure
s 5
feet
3 i
nch
es c
asts
an 8
-foo
t sh
adow
.
7.W
rite
a p
ropo
rtio
n t
hat
can
be
use
d to
det
erm
ine
the
hei
ght
of t
he
ligh
thou
se.
Sam
ple
an
swer
:If
x�
hei
gh
t o
f lig
hth
ou
se,�
5.x 25�
��12 88 �
.
8.W
hat
is
the
hei
ght
of t
he
ligh
thou
se?
84 f
t
F
GE
H
I
SR
P
QT
8N
JL
K
Mx
� 5
6x �
2
24
12
18N
P
QL
M
x �
3x
� 1
18
1612
.516
14
11
M
LN
SR
T42
�
42�
24
1812
16J
AK
YS
W
Answers (Lesson 7–3)
Chapter 7 A12 Glencoe Geometry
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Cha
pter
727
Gle
ncoe
Geo
met
ry
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Less
on R
eadi
ng G
uide
Par
alle
l Lin
es a
nd
Pro
po
rtio
nal
Par
ts
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-4
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 7
-4 i
n y
our
text
boo
k.
Use
a g
eom
etri
c id
ea t
o ex
plai
n w
hy
the
dist
ance
bet
wee
n C
hic
ago
Ave
nu
e an
dO
nta
rio
Str
eet
is s
hor
ter
alon
g M
ich
igan
Ave
nu
e th
an a
lon
g L
ake
Sh
ore
Dri
ve.
Sam
ple
an
swer
:Th
e sh
ort
est
dis
tan
ce b
etw
een
tw
o p
aral
lel l
ines
isth
e p
erp
end
icu
lar
dis
tan
ce.
Rea
d t
he
Less
on
1.P
rovi
de t
he
mis
sin
g w
ords
to
com
plet
e th
e st
atem
ent
of e
ach
th
eore
m.T
hen
sta
te t
he
nam
e of
th
e th
eore
m.
a.If
a l
ine
inte
rsec
ts t
wo
side
s of
a t
rian
gle
and
sepa
rate
s th
e si
des
into
cor
resp
ondi
ng
segm
ents
of
len
gth
s,th
en t
he
lin
e is
to
th
e
thir
d si
de.
Co
nver
se o
f th
e Tr
ian
gle
Pro
po
rtio
nal
ity
Th
eore
mb
.A
mid
segm
ent
of a
tri
angl
e is
to
on
e si
de o
f th
e tr
ian
gle
and
its
leng
th is
th
e le
ngth
of
that
sid
e.Tr
ian
gle
Mid
seg
men
t Th
eore
mc.
If a
line
is
to o
ne s
ide
of a
tri
angl
e an
d in
ters
ects
the
oth
er t
wo
side
s
in
dist
inct
poi
nts
,th
en i
t se
para
tes
thes
e si
des
into
of p
ropo
rtio
nal
len
gth
.Tr
ian
gle
Pro
po
rtio
nal
ity
Th
eore
m
2.R
efer
to
the
figu
re a
t th
e ri
ght.
a.N
ame
the
thre
e m
idse
gmen
ts o
f �
RS
T.
U�V�
,V�W�
,U�W�
b.
If R
S�
8,R
U�
3,an
d T
W�
5,fi
nd
the
len
gth
of
each
of
the
mid
segm
ents
.U
V�
5,V
W�
3,U
W�
4c.
Wh
at i
s th
e pe
rim
eter
of
�R
ST
?24
d.
Wh
at i
s th
e pe
rim
eter
of
�U
VW
?12
e.W
hat
are
th
e pe
rim
eter
s of
�R
UV
,�S
VW
,an
d �
TU
W?
12;
12;
12f.
How
are
th
e pe
rim
eter
s of
eac
h o
f th
e fo
ur
smal
l tr
ian
gles
rel
ated
to
the
peri
met
er o
fth
e la
rge
tria
ngl
e?T
he
per
imet
er o
f ea
ch s
mal
l tri
ang
le is
on
e-h
alf
the
per
imet
er o
f th
e la
rge
tria
ng
le.
g.W
ould
th
e re
lati
onsh
ip t
hat
you
fou
nd
in p
art
f ap
ply
to a
ny
tria
ngl
e in
wh
ich
th
em
idpo
ints
of
the
thre
e si
des
are
con
nec
ted?
yes
Rem
emb
er W
hat
Yo
u L
earn
ed
3.A
goo
d w
ay t
o re
mem
ber
a n
ew m
ath
emat
ical
ter
m i
s to
rel
ate
it t
o ot
her
mat
hem
atic
alvo
cabu
lary
th
at y
ou a
lrea
dy k
now
.Wh
at i
s an
eas
y w
ay t
o re
mem
ber
the
defi
nit
ion
of
mid
segm
ent
usi
ng
oth
er g
eom
etri
c te
rms?
Sam
ple
an
swer
:A
mid
seg
men
tis
ase
gm
ent
that
co
nn
ects
th
e m
idp
oin
tso
f tw
o s
ides
of
a tr
ian
gle
.
R U
V W
T
S
seg
men
tstw
op
aral
lel
on
e-h
alf
par
alle
l
par
alle
lp
rop
ort
ion
al
Lesson 7-4
Cha
pter
726
Gle
ncoe
Geo
met
ry
Enri
chm
ent
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-3
Mov
ing
Sh
adow
sH
ave
you
eve
r w
atch
ed y
our
shad
ow a
s yo
u
wal
ked
alon
g th
e st
reet
at
nig
ht
and
obse
rved
how
its
sh
ape
chan
ges
as y
ou m
ove?
Su
ppos
ea
man
wh
o is
6 f
eet
tall
is
stan
din
g be
low
a
lam
ppos
t th
at i
s 20
fee
t ta
ll.T
he
man
is
wal
kin
g aw
ay f
rom
th
e la
mpp
ost
at a
rat
e of
5
feet
per
sec
ond.
1.If
th
e m
an i
s m
ovin
g at
a r
ate
of 5
fee
t pe
rse
con
d,m
ake
a co
nje
ctu
re a
s to
th
e ra
teth
at h
is s
had
ow i
s m
ovin
g.S
amp
le a
nsw
er:
His
sh
ado
w is
mov
ing
mo
re q
uic
kly
than
he
is.
2.H
ow f
ar a
way
fro
m t
he
lam
ppos
t is
th
e m
an a
fter
8 s
econ
ds?
40 f
t
3.H
ow f
ar i
s th
e en
d of
his
sh
adow
fro
m t
he
bott
om o
f th
e la
mpp
ost
afte
r 8
seco
nds
? U
se s
imil
ar t
rian
gles
to
solv
e th
is p
robl
em.
57.1
4 ft
4.A
fter
3 m
ore
seco
nds
,how
far
fro
m t
he
lam
ppos
t is
th
e m
an?
How
far
fro
m t
he
lam
ppos
t is
his
sh
adow
?55
fee
t;78
.57
ft
5.H
ow m
any
feet
did
th
e m
an m
ove
in 3
sec
onds
? H
ow m
any
feet
did
th
e sh
adow
mov
e in
3 s
econ
ds?
15 f
eet;
21.4
3 ft
6.T
he
man
is
mov
ing
at a
rat
e of
5 f
eet/
seco
nd.
Wh
at r
ate
is h
is s
had
ow m
ovin
g?H
ow d
oes
this
rat
e co
mpa
re t
o th
e co
nje
ctu
re y
ou m
ade
in p
robl
em 1
? M
ake
aco
nje
ctu
re a
s to
wh
y th
e re
sult
s ar
e li
ke t
his
.7.
14 f
t/s;
Sam
ple
an
swer
:H
is s
had
ow
is g
etti
ng
lon
ger
as
he
mov
es f
urt
her
aw
ay f
rom
th
e la
mp
po
st.
20
ft
6 ft
x ft
5 ft
/sec
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Answers (Lessons 7–3 and 7–4)
Chapter 7 A13 Glencoe Geometry
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
An
swer
s
Cha
pter
729
Gle
ncoe
Geo
met
ry
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nued
)
Par
alle
l Lin
es a
nd
Pro
po
rtio
nal
Par
ts
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-4
Div
ide
Seg
men
ts P
rop
ort
ion
ally
Wh
en
thre
e or
mor
e pa
rall
el l
ines
cu
t tw
o tr
ansv
ersa
ls,
they
sep
arat
e th
e tr
ansv
ersa
ls i
nto
pro
port
ion
al
part
s.If
th
e ra
tio
of t
he
part
s is
1,t
hen
th
e pa
rall
elli
nes
sep
arat
e th
e tr
ansv
ersa
ls i
nto
con
gru
ent
part
s.
If �
1|| �
2|| �
3,If
�4
|| �5
|| �6
and
then
�a b��
� dc � .�u v�
�1,
then
�w x��
1.
Ref
er t
o li
nes
�1,
� 2,a
nd
�3
abov
e.If
a�
3,b
�8,
and
c�
5,fi
nd
d.
� 1|| �
2|| �
3so
�3 8��
� d5 � .T
hen
3d
�40
an
d d
�13
�1 3� .
Fin
d x
and
y.
1.2.
x�
8x
�9
3.4.
x�
5;y
�2
y�
3�1 3�
5.6.
x�
12y
�3
1632
y �
3y
34
x �
4x
5
8y
� 2
y2x
� 4
3 x �
12y
� 2
3 y
2x �
6
x �
3
12
x �
12
123x5x
a
bd
uv
xw
ct
n m
s� 1
� 4� 5
� 6
� 2
� 3
Exam
ple
Exer
cise
s
Lesson 7-4
Cha
pter
728
Gle
ncoe
Geo
met
ry
Stud
y G
uide
and
Inte
rven
tion
Par
alle
l Lin
es a
nd
Pro
po
rtio
nal
Par
ts
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Pro
po
rtio
nal
Par
ts o
f Tr
ian
gle
sIn
an
y tr
ian
gle,
a li
ne
para
llel
to
one
side
of
a tr
ian
gle
sepa
rate
s th
e ot
her
tw
o si
des
prop
orti
onal
ly.T
he
con
vers
e is
als
o tr
ue.
If X
and
Yar
e th
e m
idpo
ints
of
R �T�
and
S�T�
,th
en X�
Y�is
am
idse
gmen
tof
th
e tr
ian
gle.
Th
e T
rian
gle
Mid
segm
ent
Th
eore
mst
ates
th
at a
mid
segm
ent
is p
aral
lel
to t
he
thir
d si
de a
nd
is h
alf
its
len
gth
.
If X
Y� �
�|| R
S��
� ,th
en �R X
TX ��
� YSY T�
.
If �R X
TX ��
� YSY T�
,th
en X
Y��
�|| R
S��
� .
If X �
Y�is
a m
idse
gmen
t,th
en X
Y��
�|| R
S��
�an
d X
Y�
�1 2� RS
.
YS
T
R
X
In �
AB
C,E�
F�|| C�
B�.F
ind
x.
Sin
ce E�
F�|| C�
B�,�
FABF �
�� EA
E C�.
�x x� �2 22
��
�1 68 �
6x�
132
�18
x�
3696
�12
x8
�x
F
C
BA
18
x �
22
x �
2
6E
A t
rian
gle
has
ver
tice
sD
(3,6
),E
(�3,
�2)
,an
d F
(7,�
2).
Mid
segm
ent
G �H�
is p
aral
lel
to E�
F�.F
ind
th
e le
ngt
h o
f G �
H�.
G �H�
is a
mid
segm
ent,
so i
ts l
engt
h i
s on
e-h
alf
that
of
E �F�
.Poi
nts
Ean
d F
hav
e th
esa
me
y-co
ordi
nat
e,so
EF
�7
�(�
3) �
10.
Th
e le
ngt
h o
f m
idse
gmen
t G �
H�is
5.
Fin
d x
.
1.7
2.10
3.17
.5
4.8
5.12
6.5
7.In
Exa
mpl
e 2,
fin
d th
e sl
ope
of E�
F�an
d sh
ow t
hat
E�F�
|| G�H�
.
Th
e en
dp
oin
ts o
f G�
H�ar
e at
(0,
2) a
nd
(5,
2).T
he
slo
pe
of
G�H�
is 0
an
d t
he
slo
pe
of
E �F�
is 0
.G�H�
and
E�F�
are
par
alle
l.
3010
x �
10
x11
x �
12
x33
3010
24x
35x9
20
x
185
5x
7
Exam
ple
1Ex
amp
le 2
Exer
cise
s
Answers (Lesson 7–4)
Chapter 7 A14 Glencoe Geometry
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Cha
pter
731
Gle
ncoe
Geo
met
ry
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Prac
tice
Par
alle
l Lin
es a
nd
Pro
po
rtio
nal
Par
ts
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-4
1.If
AD
�24
,DB
�27
,an
d E
B�
18,
2.F
ind
x,Q
T,a
nd
TR
if Q
T�
x�
6,fi
nd
CE
.S
R�
12,P
S�
27,a
nd
TR
�x
�4.
1612
;18
;8
Det
erm
ine
wh
eth
er J�
K�|| N�
M�.
3.J
N�
18,J
L�
30,K
M�
21,a
nd
ML
�35
no
4.K
M�
24,K
L�
44,a
nd
NL
��5 6� J
N
yes
CO
OR
DIN
ATE
GEO
MET
RYF
or E
xerc
ises
5 a
nd
6,u
se t
he
foll
owin
g in
form
atio
n.
Tri
angl
e E
FG
has
ver
tice
s E
(�4,
�1)
,F(2
,5),
and
G(2
,�1)
.Poi
nt
Kis
th
e m
idpo
int
of E �
G�an
d H
is t
he
mid
poin
t of
F�G�
.
5.S
how
th
at E�
F�is
par
alle
l to
K�H�
.
Th
e sl
op
e o
f E�
F�is
1 a
nd
th
e sl
op
e o
f K�
H�is
1,
so E�
F�is
par
alle
l to
K�H�
.
6.S
how
th
at K
H�
�1 2� EF
.
Th
e le
ng
th o
f K�
H�is
3�
2�,an
d t
he
len
gth
of
E�F�
is 6
�2�.
7.F
ind
xan
d y.
8.F
ind
xan
d y.
x�
4,y
�9
x�
�5 2� ,y
��9 4�
9.M
APS
Th
e di
stan
ce f
rom
Wil
min
gton
to
Ash
Gro
ve a
lon
g K
enda
ll i
s 82
0 fe
et a
nd
alon
g M
agn
olia
,660
fee
t.If
th
e di
stan
ce b
etw
een
Bee
ch a
nd
Ash
Gro
ve a
lon
g M
agn
olia
is
280
feet
,wh
at i
s th
e di
stan
ce b
etw
een
th
e tw
o st
reet
s al
ong
Ken
dall
?
abo
ut
348
ft
Ash
Grov
e
Beec
h
Mag
nolia
Kend
all
Wilm
ingt
on
4 – 3y �
2
3 x �
4x
� 1
4 y �
43x
� 4
2 – 3y �
31 – 3y
� 6
5 – 4x �
3
x
y
O
EGF H
K
NL
J
KM
S
Q
TR
P
D
EC BA
Lesson 7-4
Cha
pter
730
Gle
ncoe
Geo
met
ry
Skill
s Pr
acti
ceP
aral
lel L
ines
an
d P
rop
ort
ion
al P
arts
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.If
JK
�7,
KH
�21
,an
d J
L�
6,2.
Fin
d x
and
TV
if R
U�
8,U
S�
14,
fin
d L
I.T
V�
x�
1 an
d V
S�
17.5
.
1811
;10
Det
erm
ine
wh
eth
er B�
C�|| D�
E�.
3.A
D�
15,D
B�
12,A
E�
10,a
nd
EC
�8
yes
4.B
D�
9,B
A�
27,a
nd
CE
is o
ne
thir
d of
EA
no
5.A
E�
30,A
C�
45,a
nd
AD
is t
wic
e D
B
yes
CO
OR
DIN
ATE
GEO
MET
RYF
or E
xerc
ises
6–8
,use
th
e fo
llow
ing
info
rmat
ion
.T
rian
gle
AB
Ch
as v
erti
ces
A(�
5,2)
,B(1
,8),
and
C(4
,2).
Poi
nt
Dis
th
e m
idpo
int
of A �
B�an
d E
is t
he
mid
poin
t of
A�C�
.
6.Id
enti
fy t
he
coor
din
ates
of
Dan
d E
.
D(�
2,5)
;E
(�0.
5,2)
7.S
how
th
at B�
C�is
par
alle
l to
D�E�
.
Sin
ce t
he
slo
pe
of
B�C�
is �
2 an
d t
he
slo
pe
of
D�E�
is �
2,B�
C�is
par
alle
l to
D�E�.
8.S
how
th
at D
E�
�1 2� BC
.
Th
e le
ng
th o
f D�
E�is
�11
.25
�o
r o
r �3 �
25�
� a
nd
th
e le
ng
th o
f B�
C�is
�45�
or
3 �5 �.
9.F
ind
xan
d y.
10.F
ind
xan
d y.
x�
6,y
�6.
5x
�2,
y�
4
3 – 2x �
2
x �
3
2 y �
1
3y �
52x
� 1
3y �
8y
� 5
x �
7
�45�
�2
x
y
O
AC
B
D
E
CB
ED
A
R
UV
T
S
HL
KJ
I
Answers (Lesson 7–4)
Chapter 7 A15 Glencoe Geometry
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
An
swer
s
Cha
pter
733
Gle
ncoe
Geo
met
ry
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Enri
chm
ent
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-4
Par
alle
l Lin
es a
nd
Co
ng
ruen
t P
arts
Th
ere
is a
th
eore
m s
tati
ng
that
if
thre
e pa
rall
el l
ines
cu
t of
f co
ngr
uen
t se
gmen
ts o
n o
ne
tran
sver
sal,
then
th
ey c
ut
off
con
gru
ent
segm
ents
on
an
y tr
ansv
ersa
l.T
his
can
be
show
n f
oran
y n
um
ber
of p
aral
lel
lin
es.T
he
foll
owin
g dr
afti
ng
tech
niq
ue
use
s th
is f
act
to d
ivid
e a
segm
ent
into
con
gru
ent
part
s.
A �B�
is t
o be
sep
arat
ed i
nto
fiv
e co
ngr
uen
t pa
rts.
Th
is c
an b
e do
ne
very
acc
ura
tely
wit
hou
t u
sin
g a
rule
r.A
ll t
hat
is
nee
ded
is a
com
pass
an
d a
piec
e of
not
eboo
k pa
per.
Ste
p 1
Hol
d th
e co
rner
of
a pi
ece
of n
oteb
ook
pape
r at
po
int
A.
Ste
p 2
Fro
m p
oin
t A
,dra
w a
seg
men
t al
ong
the
pape
r th
at i
s fi
ve s
pace
s lo
ng.
Mar
k w
her
e th
e li
nes
of
th
e n
oteb
ook
pape
r m
eet
the
segm
ent.
Lab
el
the
fift
h p
oin
t,P.
Ste
p 3
Dra
w P�
B�.T
hro
ugh
eac
h o
f th
e ot
her
mar
ks
on A �
P�,c
onst
ruct
a l
ine
para
llel
to
B�P�
.Th
e po
ints
wh
ere
thes
e li
nes
in
ters
ect
A �B�
wil
l di
vide
A �B�
into
fiv
e co
ngr
uen
t se
gmen
ts.
Use
a c
omp
ass
and
a p
iece
of
not
eboo
k p
aper
to
div
ide
each
seg
men
t in
to t
he
give
n n
um
ber
of
con
gru
ent
par
ts.
See
stu
den
t’s w
ork
.
1.si
x co
ngr
uen
t pa
rts
2.se
ven
con
gru
ent
part
sA
B
AB
A
P
B
AB
P
AB
AB
Lesson 7-4
Cha
pter
732
Gle
ncoe
Geo
met
ry
Wor
d Pr
oble
m P
ract
ice
Par
alle
l Lin
es a
nd
Pro
po
rtio
nal
Par
ts
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.C
AR
PEN
TRY
Jake
is
fixi
ng
an A
-fra
me.
He
wan
ts t
o ad
d a
hor
izon
tal
supp
ort
beam
hal
fway
up
and
para
llel
to
the
grou
nd.
How
lon
g sh
ould
th
isbe
am b
e?4
ft
2.ST
REE
TSIn
th
e di
agra
m,C
ay S
tree
tan
d B
ay S
tree
t ar
e pa
rall
el.F
ind
x.
1.12
km
3.JU
NG
LE G
YM
SP
rass
ad i
s bu
ildi
ng
atw
o-st
ory
jun
gle
gym
acc
ordi
ng
to t
he
plan
s sh
own
.Fin
d x.
13 f
t 4
in.
4.FI
REM
ENA
cat
is
stu
ck i
n a
tre
ean
d fi
rem
en t
ry t
ore
scu
e it
.Bas
edon
th
e fi
gure
,if
afi
rem
an c
lim
bs
to t
he
top
of t
he
ladd
er,h
ow f
araw
ay i
s th
e ca
t?34
.5 f
t
EQU
AL
PAR
TSF
or E
xerc
ises
5 a
nd
6,
use
th
e fo
llow
ing
info
rmat
ion
.N
ick
has
a s
tick
th
at h
e w
ould
lik
e to
di
vide
in
to 9
equ
al p
arts
.He
plac
es i
t on
a p
iece
of
grid
pap
er a
s sh
own
.Th
e gr
id p
aper
is
rule
d so
th
at v
erti
cal
and
hor
izon
tal
lin
es a
re e
qual
ly s
pace
d.
5.E
xpla
in h
ow h
e ca
n u
se t
he
grid
pap
erto
hel
p h
im f
ind
wh
ere
he
nee
ds t
o cu
tth
e st
ick.
Bec
ause
he
po
siti
on
ed t
he
stic
kso
th
at it
s en
ds
are
tou
chin
gh
ori
zon
tal l
ines
th
at a
re 9
un
its
apar
t,h
e ca
n c
ut
the
stic
kw
her
ever
oth
er h
ori
zon
tal l
ines
inte
rsec
t it
.
6.S
upp
ose
Nic
k w
ants
to
divi
de h
is s
tick
into
5 e
qual
par
ts u
tili
zin
g th
e gr
idpa
per.
Wh
at c
an h
e do
?H
e ca
n r
ota
te t
he
stic
k so
itto
uch
es h
ori
zon
tal l
ines
5 u
nit
sap
art
and
ap
ply
th
e sa
me
met
ho
d.
Mee
eeow
ww
!
30 ft
.
40 ft
.46
ft.x
8 ft.
8 ft.
10 ft
.
24 ft.
10 ft
.x
Cay
St.
1 km
1.4
km
0.8
km
Bay
St.
Dale St.
Earl St.
(not
dra
wn
to s
cale
)
x
8 fe
et
Answers (Lesson 7–4)
Chapter 7 A16 Glencoe Geometry
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Cha
pter
735
Gle
ncoe
Geo
met
ry
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
Par
ts o
f S
imila
r Tri
ang
les
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-5
Peri
met
ers
If t
wo
tria
ngl
es a
re s
imil
ar,t
hei
r pe
rim
eter
s h
ave
the
sam
e pr
opor
tion
as
the
corr
espo
ndi
ng
side
s.
If �
AB
C�
�R
ST
,th
en
�A RB S
� �B S
TC��
RATC
��
�A RB S�
��B S
TC ��
� RAC T�
.
Use
th
e d
iagr
am a
bov
e w
ith
�A
BC
��
RS
T.I
f A
B�
24 a
nd
RS
�15
,fi
nd
th
e ra
tio
of t
hei
r p
erim
eter
s.S
ince
�A
BC
��
RS
T,t
he
rati
o of
th
e pe
rim
eter
s of
�A
BC
and
�R
ST
is t
he
sam
e as
th
era
tio
of c
orre
spon
din
g si
des.
Th
eref
ore
��2 14 5�
��8 5�
Eac
h p
air
of t
rian
gles
is
sim
ilar
.Fin
d t
he
per
imet
er o
f th
e in
dic
ated
tri
angl
e.
1.�
XY
Z2.
�B
DE
3345
3.�
AB
C4.
�X
YZ
8455
.4
5.�
AB
C6.
�R
ST
5411
0
25 20
10
PT
SM
R
95
13
12
AD
E
C
B
56
8.7
13
10
XY
ZT
RS
18
202515
17 8
NB
AC
PM
36
9 11 CDE
A
B
44
24
2022
10
TR
XZ
YS
peri
met
er o
f �
AB
C�
��
peri
met
er o
f �
RS
T
AC
BS
RT
Exam
ple
Exer
cise
s
Lesson 7-5
Cha
pter
734
Gle
ncoe
Geo
met
ry
Less
on R
eadi
ng G
uide
Par
ts o
f S
imila
r Tri
ang
les
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 7
-5 i
n y
our
text
boo
k.
•H
ow i
s si
mil
arit
y in
volv
ed i
n t
he
proc
ess
of m
akin
g a
phot
ogra
phic
pri
nt
from
an
egat
ive?
Sam
ple
an
swer
:Th
e p
rin
t is
an
en
larg
ed v
ersi
on
of
the
neg
ativ
e.T
he
imag
e o
n t
he
pri
nt
is s
imila
r to
th
e im
age
on
th
e n
egat
ive,
sow
hen
yo
u lo
ok
at t
he
pri
nt,
you
will
see
exa
ctly
th
e sa
me
thin
gs
inth
e sa
me
pro
po
rtio
ns
as o
n t
he
neg
ativ
e,ju
st la
rger
.•
Wh
y do
ph
otog
raph
ers
plac
e th
eir
cam
eras
on
tri
pods
?
Sam
ple
an
swer
:Th
ree
po
ints
det
erm
ine
a p
lan
e,so
th
e th
ree
feet
of
the
trip
od
are
co
pla
nar
an
d t
he
trip
od
will
no
t w
ob
ble
.
Rea
d t
he
Less
on
1.In
th
e fi
gure
,�R
ST
��
UV
W.C
ompl
ete
each
pr
opor
tion
in
volv
ing
the
len
gth
s of
seg
men
ts i
nth
is f
igu
re b
y re
plac
ing
the
ques
tion
mar
k.T
hen
iden
tify
th
e de
fin
itio
n o
r th
eore
m f
rom
th
e li
stbe
low
th
at t
he
com
plet
ed p
ropo
rtio
n i
llu
stra
tes.
i.D
efin
itio
n o
f co
ngr
uen
t po
lygo
ns
ii.
Def
init
ion
of
sim
ilar
pol
ygon
s
iii.
Pro
port
ion
al P
erim
eter
s T
heo
rem
iv.
An
gle
Bis
ecto
rs T
heo
rem
v.S
imil
ar t
rian
gles
hav
e co
rres
pon
din
g al
titu
des
prop
orti
onal
to
corr
espo
ndi
ng
side
s.
vi.
Sim
ilar
tri
angl
es h
ave
corr
espo
ndi
ng
med
ian
s pr
opor
tion
al t
o co
rres
pon
din
g si
des.
vii.
Sim
ilar
tria
ngle
s ha
ve c
orre
spon
ding
ang
le b
isec
tors
pro
port
iona
l to
corr
espo
ndin
g si
des.
a.�R
S�
S ?T�
TR
��
� URS V�
UV
�V
W�
WU
;iii
b.
� URWT �
��S ?X �
VY
;v
c.�R U
M N��
� V? W�S
T;
vid
.� UR
S V��
�S ?T �V
W;
ii
e.�R P
SP ��
� S? T�R
T;
ivf.
�U ?N ��
�U RW T�
RM
;vi
g.� WT
P Q��
�R ?T �U
W;
vii
h.
�U VWW �
�� Q? V�
UQ
;iv
Rem
emb
er W
hat
Yo
u L
earn
ed
2.A
goo
d w
ay t
o re
mem
ber
a la
rge
amou
nt
of i
nfo
rmat
ion
is
to r
emem
ber
key
wor
ds.W
hat
key
wor
ds w
ill
hel
p yo
u r
emem
ber
the
feat
ure
s of
sim
ilar
tri
angl
es t
hat
are
pro
port
ion
alto
th
e le
ngt
hs
of t
he
corr
espo
ndi
ng
side
s?
per
imet
ers,
alti
tud
es,a
ng
le b
isec
tors
,med
ian
s
W
QN
YU
V
T
PM
XR
S
Answers (Lesson 7–5)
Chapter 7 A17 Glencoe Geometry
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
An
swer
s
Cha
pter
737
Gle
ncoe
Geo
met
ry
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Skill
s Pr
acti
ceP
arts
of
Sim
ilar T
rian
gle
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-5
Fin
d t
he
per
imet
er o
f th
e gi
ven
tri
angl
e.
1.�
JK
L,i
f �
JK
L�
�R
ST
,RS
�14
,2.
�D
EF
,if
�D
EF
��
AB
C,A
B�
27,
ST
�12
,TR
�10
,an
d L
J�
14B
C�
16,C
A�
25,a
nd
FD
�15
50.4
40.8
3.�
PQ
R,i
f �
PQ
R�
�L
MN
,LM
�16
,4.
�K
LM
,if
�K
LM
��
FG
H,F
G�
30,
MN
�14
,NL
�27
,an
d R
P�
18G
H�
38,H
F�
38,a
nd
KL
�24
3884
.8
Use
th
e gi
ven
in
form
atio
n t
o fi
nd
eac
h m
easu
re.
5.F
ind
FG
if �
RS
T�
�E
FG
,S�H�
is a
n
6.F
ind
MN
if �
AB
C�
�M
NP,
A�D�
is a
n
alti
tude
of
�R
ST
,F �J�
is a
n a
ltit
ude
of
alti
tude
of
�A
BC
,M�Q�
is a
n a
ltit
ude
of
�E
FG
,ST
�6,
SH
�5,
and
FJ
�7.
�M
NP
,AB
�24
,AD
�14
,and
MQ
�10
.5.
8.4
18
Fin
d x
.
7.�
HK
L�
�X
YZ
8.
8�1 3�
8.4
LH
K
18
10
Y
15
x
ZX
7
20
24
x
C
A
BD
PN
QM
JG
E
F
HT
R
S
GL K
M
F
H
LM
PQ
RN
A
BC
D
EF
RS
T
JK
L
Lesson 7-5
Cha
pter
736
Gle
ncoe
Geo
met
ry
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nued
)
Par
ts o
f S
imila
r Tri
ang
les
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Spec
ial S
egm
ents
of
Sim
ilar
Tria
ng
les
Wh
en t
wo
tria
ngl
es a
re s
imil
ar,
corr
espo
ndi
ng
alti
tude
s,an
gle
bise
ctor
s,an
d m
edia
ns
are
prop
orti
onal
to
the
corr
espo
ndi
ng
side
s.A
lso,
in a
ny
tria
ngl
e an
an
gle
bise
ctor
sep
arat
es t
he
oppo
site
sid
e in
to s
egm
ents
th
ath
ave
the
sam
e ra
tio
as t
he
oth
er t
wo
side
s of
th
e tr
ian
gle.
In t
he
figu
re,
�A
BC
��
XY
Z,w
ith
an
gle
bis
ecto
rs a
ssh
own
.Fin
d x
.
Sin
ce �
AB
C�
�X
YZ
,th
e m
easu
res
of t
he
angl
e bi
sect
ors
are
prop
orti
onal
to
the
mea
sure
s of
a p
air
of c
orre
spon
din
g si
des.
�A XB Y�
�� YB
WD �
�2 x4 ��
�1 80 �
10x
�24
(8)
10x
�19
2x
�19
.2
2410 D
W
Y
ZX
C
B
A
8x
S�U�
bis
ects
�R
ST
.Fin
d x
.
Sin
ce S �
U�is
an
an
gle
bise
ctor
,�R T
UU ��
�R TSS �
.
� 2x 0��
�1 35 0�
30x
�20
(15)
30x
�30
0x
�10
x2030
15
UT
S
R
Fin
d x
for
each
pai
r of
sim
ilar
tri
angl
es.
1.2.
108
3.4.
2.25
8.75
5.6.
12�5 6�
15
2x �
2x
� 1
2816
17
11
x �
7
x
10
10x
8
87
3
3
4x
69
12x
x
36
1820
Exam
ple
1Ex
amp
le 2
Exer
cise
s
Answers (Lesson 7–5)
Chapter 7 A18 Glencoe Geometry
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Cha
pter
739
Gle
ncoe
Geo
met
ry
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Wor
d Pr
oble
m P
ract
ice
Par
ts o
f S
imila
r Tri
ang
les
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-5
Lesson 7-5
1.JO
GG
ING
Mac
y w
ants
to
jog
arou
nd
Tri
angl
e P
ark.
On
a s
cale
map
,th
e pa
rkh
as a
per
imet
er o
f 11
in
ches
.Th
e sc
ale
of t
he
map
is
1 in
ch :
100
yard
s.W
hat
is
the
peri
met
er o
f th
e ac
tual
par
k?11
00 y
d
2.TE
NTS
Jan
a w
ent
cam
pin
g an
d st
ayed
in a
ten
t sh
aped
lik
e a
tria
ngl
e.In
aph
oto
of t
he
ten
t,th
e ba
se o
f th
e te
nt
is6
inch
es a
nd
the
alti
tude
is
5 in
ches
.Th
eac
tual
bas
e w
as 1
2 fe
et l
ong.
Wh
at w
asth
e h
eigh
t of
th
e ac
tual
ten
t?
10 f
t
3.PL
AY
GR
OU
ND
Th
e pl
aygr
oun
d at
Han
k’s
sch
ool
has
a l
arge
rig
ht
tria
ngl
epa
inte
d in
th
e gr
oun
d.H
ank
star
ts
at t
he
righ
t an
gle
corn
er a
nd
wal
ksto
war
d th
e op
posi
te s
ide
alon
g an
an
gle
bise
ctor
an
d st
ops
wh
en h
e ge
ts t
o th
eh
ypot
enu
se.
How
mu
ch f
arth
er f
rom
Han
k is
poi
nt
Bve
rsu
s po
int
A?
7�1 7�
ft
4.FL
AG
PO
LES
A f
lag
pole
att
ach
ed t
oth
e si
de o
f a
buil
din
g is
su
ppor
ted
wit
h
a n
etw
ork
of s
trin
gs a
s sh
own
in
th
efi
gure
.
Th
e ri
ggin
g is
don
e so
th
at A
E�
EF
,A
C�
CD
,an
d A
B�
BC
.Wh
at i
s th
era
tio
of C
Fto
BE
?2
:1
CO
PIES
For
Exe
rcis
es 5
an
d 6
,use
th
efo
llow
ing
info
rmat
ion
.G
ordo
n m
ade
a ph
otoc
opy
of a
pag
e fr
om
his
geo
met
ry b
ook
to e
nla
rge
one
of t
he
figu
res.
Th
e ac
tual
fig
ure
th
at h
e co
pied
is
show
n b
elow
.
Th
e ph
otoc
opy
cam
e ou
t po
orly
.Gor
don
cou
ld n
ot r
ead
the
nu
mbe
rs o
n t
he
phot
ocop
y,al
thou
gh t
he
tria
ngl
e it
self
w
as c
lear
.Gor
don
mea
sure
d th
e ba
se o
f th
e en
larg
ed t
rian
gle
and
fou
nd
it t
o be
20
0 m
illi
met
ers.
5.W
hat
is
the
len
gth
of
the
draw
n a
ltit
ude
of t
he
enla
rged
tri
angl
e? R
oun
d yo
ur
answ
er t
o th
e n
eare
st m
illi
met
er.
149
mm
6.W
hat
is
the
len
gth
of
the
draw
n m
edia
nof
th
e en
larg
ed t
rian
gle?
Rou
nd
you
ran
swer
to
the
nea
rest
mil
lim
eter
.15
4 m
m
39 m
mMedian
Altitude
30 m
m
29 m
m
AB
C
DF E
A
B
45˚
30 ft
40 ft
50 ft
x
Cha
pter
738
Gle
ncoe
Geo
met
ry
Prac
tice
Par
ts o
f S
imila
r Tri
ang
les
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Fin
d t
he
per
imet
er o
f th
e gi
ven
tri
angl
e.
1.�
DE
F,i
f �
AB
C�
�D
EF
,AB
�36
,2.
�S
TU
,if
�S
TU
��
KL
M,K
L�
12,
BC
�20
,CA
�40
,an
d D
E�
35L
M�
31,M
K�
32,a
nd
US
�28
93.3�
65.6
25
Use
th
e gi
ven
in
form
atio
n t
o fi
nd
eac
h m
easu
re.
3.F
ind
PR
if �
JK
L�
�N
PR
,K�M�
is a
n
4.F
ind
ZY
if �
ST
U�
�X
YZ
,U�A�
is a
n
alti
tude
of
�J
KL
,P �T�
is a
n a
ltit
ude
of
alti
tude
of
�S
TU
,Z�B�
is a
n a
ltit
ude
of
�N
PR
,KL
�28
,KM
�18
,an
d �
XY
Z,U
T�
8.5,
UA
�6,
and
PT
�15
.75.
ZB
�11
.4.
24.5
16.1
5
Fin
d x
.
5.6.
13.5
16.8
PHO
TOG
RA
PHY
For
Exe
rcis
es 7
an
d 8
,use
th
e fo
llow
ing
info
rmat
ion
.F
ran
cin
e h
as a
cam
era
in w
hic
h t
he
dist
ance
fro
m t
he
len
s to
th
e fi
lm i
s 24
mil
lim
eter
s.
7.If
Fra
nci
ne
take
s a
full
-len
gth
ph
otog
raph
of
her
fri
end
from
a d
ista
nce
of
3 m
eter
s an
dth
e h
eigh
t of
her
fri
end
is 1
40 c
enti
met
ers,
wh
at w
ill
be t
he
hei
ght
of t
he
imag
e on
th
efi
lm?
(Hin
t:C
onve
rt t
o th
e sa
me
un
it o
f m
easu
re.)
11.2
mm
8.S
upp
ose
the
hei
ght
of t
he
imag
e on
th
e fi
lm o
f h
er f
rien
d is
15
mil
lim
eter
s.If
Fra
nci
ne
took
a f
ull
-len
gth
sh
ot,w
hat
was
th
e di
stan
ce b
etw
een
th
e ca
mer
a an
d h
er f
rien
d?2.
24 m
x28
2030
402x
� 1
25x
� 4
YX
BZ
TS
AU
MJ
L
K
TN
R
P
KS
LT
UM
B E
CF
DA
Answers (Lesson 7–5)
Chapter 7 A19 Glencoe Geometry
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
An
swer
s
Cha
pter
741
Gle
ncoe
Geo
met
ry
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Spre
adsh
eet
Act
ivit
yF
ract
als
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-5
You
can
use
a s
prea
dsh
eet
to c
reat
e a
Sie
rpin
ski t
rian
gle.
Use
a s
pre
adsh
eet
to c
reat
e a
Sie
rpin
ski
tria
ngl
e.
Ste
p 1
In c
ell A
2,en
ter
1.In
cel
l A3,
ente
r an
equ
als
sign
fol
low
ed b
y A
2�1
.Th
is w
ill
retu
rn t
he
nu
mbe
r of
ite
rati
ons.
Cli
ck o
n t
he
bott
om r
igh
t co
rner
of
cell
A2
and
drag
it
thro
ugh
cel
l A50
0 to
get
500
ite
rati
ons.
Ste
p 2
In c
ell
B1,
ente
r 0.
5.T
his
in
dica
tes
the
mid
poin
ts o
f th
e se
gmen
ts.
Ste
p 3
In c
ell
C1,
ente
r 1
and
in c
ell
D1,
ente
r 0.
3.S
tep
4In
cel
l B
2,en
ter
an e
qual
s si
gn f
ollo
wed
by
3*R
AN
D()
.Cli
ck o
n t
he
bott
om r
igh
tco
rner
of
cell
B2
and
drag
in
th
rou
gh c
ell
B50
0 to
get
500
ite
rati
ons.
Ste
p 5
In c
ell
C2,
ente
r an
equ
als
sign
fol
low
ed b
y th
e re
curs
ive
form
ula
IF(B
2<1,
(1�
$B$1
)*C
1,IF
(B2�
2,(1
�$B
$1)*
C1�
$B$1
,(1�
$B$1
)*C
1�2*
$B$1
)).T
his
wil
l re
turn
th
e x
valu
es o
f th
e po
ints
to
be g
raph
ed.C
lick
on
th
e bo
ttom
rig
ht
corn
er o
f ce
ll C
2 an
d dr
ag t
hro
ugh
cel
l C
500.
Ste
p 6
In c
ell
D2,
ente
r an
equ
als
sign
fol
low
ed b
y th
e re
curs
ive
form
ula
IF(B
2�1,
(1�
$B$1
)*D
1,IF
(B2�
2,(1
�$B
$1)*
D1�
$B$1
,(1�
$B$1
)*D
1)).
Th
is w
ill
retu
rn t
he
yva
lues
of
the
poin
ts t
o be
gra
phed
.Cli
ck o
n t
he
bott
om r
igh
t co
rner
of
cell
D2
and
drag
th
rou
ghce
ll D
500.
Ste
p 7
To
grap
h t
he
valu
es i
nco
lum
ns
C a
nd
D,f
irst
h
igh
ligh
t al
l of
th
e da
ta
in t
he
two
colu
mn
s.N
ext,
choo
se t
he
char
t w
izar
dfr
om t
he
tool
bar.
Sel
ect
XY
(Sca
tter
).P
ress
Nex
t,N
ext.
Th
en s
elec
t th
e G
ridl
ines
tab
and
un
chec
k th
e M
ajor
gri
dlin
es.T
hen
pre
ss N
ext
and
Fin
ish
.T
his
wil
l re
turn
th
e S
ierp
insk
i tr
ian
gle.
An
alyz
e yo
ur
dra
win
g.1.
Wh
at h
appe
ns
to y
our
draw
ing
if y
ou h
ave
mor
e it
erat
ion
s? T
ry 1
000,
2000
,an
d 50
00.
Th
e p
ictu
re lo
oks
sh
arp
er w
ith
mo
re it
erat
ion
s.2.
Ch
ange
th
e 0.
5 to
2\3
in c
ell B
1.(H
int:
You
may
nee
d to
en
ter
0.66
6666
for
2\3
.) H
owdo
es t
his
ch
ange
th
e pi
ctu
re?
See
stu
den
ts’w
ork
.3.
Ch
ange
0.3
to
0.6
in c
ell D
1.H
ow d
oes
this
ch
ange
th
e dr
awin
g?
See
stu
den
ts’w
ork
.4.
En
ter
the
foll
owin
g in
to a
new
spr
eads
hee
t an
d de
scri
be w
hat
you
see
.S
tep
1:In
cel
l A2,
ente
r th
e fo
rmu
la �
A1.
Ste
p 2:
In c
ell B
2,en
ter
the
form
ula
� A
1�B
1.S
tep
3:C
lick
on
th
e bo
ttom
rig
ht
corn
er o
f ce
ll B
2 an
d dr
ag t
hro
ugh
cel
l L2.
Ste
p 4:
Fir
st,c
lick
on
th
e 2
nex
t to
cel
l A2.
Th
en,c
lick
on
th
e bo
ttom
left
cor
ner
of
2an
d dr
ag d
own
th
rou
gh c
ell 1
2.S
tep
5:In
cel
l A1,
ente
r a
1 an
d pr
ess
EN
TE
R.
Pas
cal’s
tri
ang
le
Sh
eet
1S
hee
t 2
Sh
eet
3
Lesson 7-5
Exam
ple
Exer
cise
s
An
oth
er P
roo
f o
f P
yth
ago
rean
Th
eore
m
1.F
or r
igh
t tr
ian
gle
AB
Cw
ith
rig
ht
angl
e C
,an
d al
titu
de C �
D�as
sh
own
at
the
righ
t,n
ame
thre
e si
mil
ar t
rian
gles
.
�A
BC
��
AC
D�
�C
BD
2.L
ist
the
thre
e si
mil
ar t
rian
gles
as
hea
din
gs i
n
the
tabl
e be
low
.Use
th
e fi
gure
to
com
plet
e th
eta
ble
to l
ist
the
corr
espo
ndi
ng
part
s of
th
e th
ree
sim
ilar
rig
ht
tria
ngl
es.
3.U
se t
he
corr
espo
ndi
ng
part
s of
th
ese
sim
ilar
tri
angl
es a
nd
thei
r pr
opor
tion
s to
com
plet
e th
e st
atem
ents
in
th
e pr
oof
and
alge
brai
call
y pr
ove
the
Pyt
hag
orea
n T
heo
rem
.
Sta
tem
ents
Rea
son
s
1.R
igh
t tr
ian
gle
AB
Cw
ith
1.
Giv
enal
titu
te C �
D�.
2.�a c�
� �d a� ,
�b c��
� be �2.
Cor
resp
ondi
ng
part
s of
sim
ilar
tria
ngl
es a
re i
n t
he
sam
e ra
tio
3.a
2�
cd
,b2
� c
e3.
Cro
ss P
rodu
cts
4.a
2�
b2
� c
d�
b2
4.A
ddit
ion
Pro
pert
y of
Equ
alit
y
5.a
2�
b2
� c
d�
ce
5.S
ubs
titu
tion
6.a
2�
b2
� c
(d�
e)
6.D
istr
ibu
tion
Pro
pert
y
7.d
� e
� c
7.S
egm
ent
addi
tion
8.a2
�b2
�c2
8.S
ubs
titu
tion
A
ab
de
c
B
C D
Cha
pter
740
Gle
ncoe
Geo
met
ry
Enri
chm
ent
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
�A
BC
�A
CD
�C
BD
Sh
ort
Leg
ah
dL
on
g L
egb
eh
Hyp
ote
nu
sec
ba
Answers (Lesson 7–5)
Chapter 7 A20 Glencoe Geometry
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.Chapter 7 Assessment Answer Key
Quiz 1 (Lessons 7–1 and 7–2) Quiz 3 (Lesson 7–4) Mid-Chapter TestPage 45 Page 46 Page 47
Quiz 2 (Lesson 7–3) Quiz 4 (Lesson 7–5)Page 45 Page 46
1.
2.
3.
4.
5.
1:30
33 in.
�BAC � �QPR or�ABC � �QPR by
SAS.
x � 4;scale factor 5:4
B
1.
2.
3.
4.
5.
yes; AA
No; the sides arenot proportional.
�ABD � �CDE or�ADB � �CDF;
8
22�12
� ft
6
1.
2.
3.
4.
5.
Not parallel because
�MJM
K� � �
NJN
L�
13�13
�
20
9
T(3, 2), U(3, �1)
1.
2.
3.
4.
5.
22�12
�
8.0 cm
corresp. altitudesare proportional tothe corresp. sides
5.3 cm
14
6.
7.
8.
9.
10.
No; SAS doesnot apply.yes; SAS
28; �83
�
120
3.6 in.
1.
2.
3.
4.
5.
B
J
C
J
B
Chapter 7 A21 Glencoe Geometry
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
An
swer
s
Chapter 7 Assessment Answer KeyVocabulary Test Form 1Page 48 Page 49 Page 50
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
ratio
scale factor
midsegment
extremes
means
false; similarpolygons
false; proportion
true
Sample answer:product of means isequal to product of
extremes
Sample answer:a segment with
endpoints that are themidpoints of any two
sides of a triangle
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
A
J
B
G
B
J
B
H
A
G
11.
12.
13.
14.
15.
16.
17.
18.
19.
B:
D
J
A
G
A
G
D
H
D
9.6
Chapter 7 A22 Glencoe Geometry
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panies, Inc.Chapter 7 Assessment Answer Key
Form 2A Form 2BPage 51 Page 52 Page 53 Page 54
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
A
F
D
H
B
H
C
F
C
G
11.
12.
13.
14.
15.
16.
17.
18.
B:
D
J
B
G
C
F
A
F
32
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
A
H
B
J
B
G
D
G
B
H
11.
12.
13.
14.
15.
16.
17.
18.
B:
D
F
C
J
B
F
D
H
26
Chapter 7 A23 Glencoe Geometry
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Chapter 7 Assessment Answer KeyForm 2CPage 55 Page 56
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
3:7
Yes; corres. �are �.
30 ft
18
42.5 ft
6.3
18.2
No; the sides arenot proportional.
72
�PQR � �STR
2�12
�
12.
13.
14.
15.
16.
17.
18.
B:
9.5
42
47
2
3
14.4
4
7
Chapter 7 A24 Glencoe Geometry
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Form 2DPage 57 Page 58
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
5:11
No; thecorresponding
sides and � arenot proportional.
48 ft
�43
�
183�13
� ft
5.5
15
yes; SSSSimilarity
75
�XYZ � �XNM
7.5
12.
13.
14.
15.
16.
17.
18.
B:
2.2
96
85
9.5
2
5�58
�
28
4.8
Chapter 7 A25 Glencoe Geometry
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Chapter 7 Assessment Answer KeyForm 3Page 59 Page 60
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
4:3
No; corr. sides arenot proportional.
yes; SAS
30 cm by 7.5 cm
5.85
5
104 in.
82
48
�83
�
5
12.
13.
14.
15.
16.
17.
18.
B:
11�37
�
7.2
�85
�
60
24.8
24 ft
9
25.6
Chapter 7 A26 Glencoe Geometry
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Extended-Response Test, Page 61Scoring Rubric
Score General Description Specific Criteria
• Shows thorough understanding of the concepts of ratios,properties of proportions, similar figures, similar triangles,dividing segments into parts, proportional parts of triangles,corresponding perimeters and altitudes, fractals, anditeration.
• Uses appropriate strategies to solve problems.• Computations are correct.• Written explanations are exemplary.• Figures are accurate and appropriate.• Goes beyond requirements of some or all problems.
• Shows an understanding of the concepts of ratios,properties of proportions, similar figures, similar triangles,dividing segments into parts, proportional parts oftriangles, corresponding perimeters and altitudes, fractals,and iteration.
• Uses appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are effective.• Figures are mostly accurate and appropriate.• Satisfies all requirements of problems.
• Shows an understanding of most of the concepts of ratios,properties of proportions, similar figures, similar triangles,dividing segments into parts, proportional parts of triangles,corresponding perimeters and altitudes, fractals, anditeration.
• May not use appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are satisfactory.• Figures are mostly accurate.• Satisfies the requirements of most of the problems.
• Final computation is correct.• No written explanations or work is shown to substantiate
the final computation.• Figures may be accurate but lack detail or explanation.• Satisfies minimal requirements of some of the problems.
• Shows little or no understanding of most of the concepts ofratios, properties of proportions, similar figures, similartriangles, dividing segments into parts, proportional partsof triangles, corresponding perimeters and altitudes,fractals, and iteration.
• Does not use appropriate strategies to solve problems.• Computations are incorrect.• Written explanations are unsatisfactory.• Figures are inaccurate or inappropriate.• Does not satisfy requirements of problems.• No answer may be given.
0 UnsatisfactoryAn incorrect solutionindicating no mathematicalunderstanding of theconcept or task, or nosolution is given
1 Nearly Unsatisfactory A correct solution with nosupporting evidence orexplanation
2 Nearly SatisfactoryA partially correctinterpretation and/orsolution to the problem
3 SatisfactoryA generally correct solution,but may contain minor flawsin reasoning or computation
4 SuperiorA correct solution that is supported by well-developed, accurateexplanations
Chapter 7 A27 Glencoe Geometry
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Chapter 7 Assessment Answer KeyExtended-Response Test, Page 61
Sample Answers
In addition to the scoring rubric found on page A26, the following sample answers may be used as guidance in evaluating open-ended assessment items.
1. �160� � �
53� or �
120� � �
135�
2. a. 3:2:2 (Note: Check to be sure that the sum of any two sides of thetriangle is greater than the third side. For example, a ratio of 1:1:2would not be acceptable.)
b. 18, 12, 12
c. 12, 8, 8
3. �ABH � �CDI � �GFI � �ADG � �GDE � �CFE � �AGE by the AAPostulate.
4.
5. a.
Mark the midpoint of each side of �PQR. Connect these points to form�XYZ. Since each segment of �XYZ is a midsegment of �PQR, itslength will be half the corresponding side, and therefore the perimeterwill be half the perimeter of �PQR.
b.
c. Each of the triangles are similar by SSS (since their sides are half thelength of the preceding sides), so the figure is strictly self-similar andthus a fractal.
d. 6
P R
Q
X
Y Z
P R
Q
X
Y Z
FD
CA
B
1
1E
4–3
3–4
Chapter 7 A28 Glencoe Geometry
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Standardized Test PracticePage 62 Page 63
1.
2.
3.
4.
5.
6.
7. A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
8.
9.
10.
11.
12. F G H J
A B C D
F G H J
A B C D
F G H J
13.
14.
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
61 .
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
821 .
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
Chapter 7 A29 Glencoe Geometry
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An
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Chapter 7 Assessment Answer KeyStandardized Test Practice (continued)Page 64
15.
16.
17.
18.
19.
20a.
20b.
20c.
�3
85.5
11 � x � 53
64.5 cm
congruent;TU � WX � �40�UV � XY � �53�VT � YU � �41�
ST � 6.32,PR � 28.46
slope of ST � �13
�,
slope of PR � �3
perpendicular
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