Mid-Term Review Packet

Name

The mid-term scheduled to be given on 11/8/12 will count as a major test grade and may

replace your lowest test grade if higher provided that you complete 100% of this packet with all

appropriate work and turn it in at the time of the test. No late review packet will be accepted.

Ifyou fail to complete even a single problem in this packet, your grade will not be replaced. All

students are to complete their own packet and not copy from other students.

By signing below, I understand the condition of this midterm as stated above.

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Lesson Practicemim1i».m,,iMiji^»gli.»mwimMiimm-i.ai—^iui»a^

Choose the correct answer.

1. What is the sumof the exterior anglemeasures in an irregular pentagon?

A. 180°

B. 360°

C. 540°

D. 900°

2. What is the value ofx in the diagram below?

3. What is the measure of eachinteriorangleof a regular octagon?

A. 360°

B. 180°

C. 135°

D. 120°

136

Use the hexagon below for questions 4-6.

4. What is the sum of the measures of the

interiorangles in the hexagon?

A. 180°

B. 360°

C. 720°

D. 900°

5. What is the measure of L1 ?

A. 135°

B. 120°

C. 45°

D. 40°

6. What is the measure of Z.2?

A. 90°

B. 95°

C. 185°

D. 320°

Duplicating any part of this book is prohibited by law. ]

Lesson Practice£jN^W^UOjlgi^££iiyi^j^ij^^^jjj^jgjJj^£

Choose the correct answer.

1. Amandine is making a triangular-shapedpizza. One sideis 12 inches longandanothersideis24 inches long. Whichofthe following could be the length of thethird side?

A. 40 inches

B. 36 inches

C. 26 inches

D. 10 inches

The sides of AXYZ are a, b, and c units

long. Use this triangle to answer questions

2 and 3.

2. Which statementabout this triangle is true?

A. Side XZ is the shortest side.

B. Side YZ is the shortest side.

C. Side XZis the longest side.

D. Side YZ is the longest side.

3. Whichstatement about the lengths of thesides is true?

A. a > c

B. a<c

C. a<b

D. a > b + c

140

Use AflST below for questions 4 and 5.

4. Which could NOT be the measure of

sLTSR?.

A. 65°

B. 71°

C. 75°

D. 91°

5. Which statement must be true about the

measure of Z.SR71

A. It isgreater thanx°and less than 90°,

B. It is less than x° and less than 90°.

C. It isgreater than x°and greaterthan 90°.

D. It is less than x° and equal to 90°.

6. Whichof the following areNOT threepossible side lengths fora triangle?

A. 6 inches, 7 inches, and 8 inches

B. 6 inches, 10 inches, and 14 inches

C. 6 inches, 11 inches, and 18 inches

D. 6 inches, 12 inches, and 16 inches

Duplicating any part of this bookis prohibited by law.J

Lesson Practice•i -^ ^-T1f^-t^ -•ttWGjto ^'j^Aava&yAu^jw; u!>mjjw.'ai: •• k>. •^av/.^tj(^St^f^s^S^1 itiJiLL^fe-S^L^aiij

3

Choose the correct answer.

1. Using onlythe information shown in thediagrams below, which triangles can bePROVEN congruent?

II

A. I only

B. I and II only

C. I and III only

D. I, II, and III

2. Using onlythe information in the diagram,which statement would help prove that thetriangles shown below arecongruent?

A. LJKM=LKLM

B. L]KM=LLKM

C. JR=KM

D. KM=KM

146

3. Which would NOT help you proveLEIH =AGFHby the HL Theorem?

a Hn

I

A. mLHEI=mLFGH=W

B. W=GH

C. LEHI=LGFH

D. 1H=FH

In this diagram, point H is the midpoint ofGK. Use this for questions 4 and 5.

4. Whichstatement can be used to prove thatthe triangles shown above arecongruent?

A. GH=GK

B. ~GK=HK

C. GH=KM

D. GH=HK

5. What is the value ofx, in units?

A. 3

B. 5

C. 7

D. 9

Duplicating any part of this book is prohibited by law. J

Lesson PracticeVfe -^I^^J^)WT^Hm^,W^

Choose the correct answer.

1. In the diagram below, lines DE, FG, and HJare perpendicular bisectors of AABC. Whichdescribes point A?

A. centroid

B. circumcenter

C. incenter

D. orthocenter

Point D is the centroid of AKLM below. Use

this diagram for questions 2 and 3.

2. If KC= 22 units,what is the lengthof CM>

A. 11 units

B. 20 units

C. 22 units

D. 44 units

3. IfMD = 20 units, what is the lengthof DAI

A. 40 units

B. 30 units

152

C. 20 units

D. 10 units

i-M^/t^w^-» vvjj^&n&L^&yi&irtgMp^y&v)

4. Point Z is the orthocenter of A TUV. Which

term accurately describes 7Y?

A. altitude

B. angle bisector

C. median of triangle

D. perpendicular bisector

Use the map below for questions 5 and 6.

Briarville

Avon Peach Road Claytown

5. A museum isequidistant from each of thethree roads shown on the map.Which couldbe used to find the museums location?

A. centroid

B. circumcenter

C. incenter

D. orthocenter

6. A school isequidistant from each of thethree towns shown on the map. Whichcould be used to find the school's location?

A. centroid

B. circumcenter

C. incenter

D. orthocenter

Duplicating any part of this bookis prohibited by law.1

Lesson Practice

Choose the correct answer.

1. Whichof the following terms CANNOT beused to describe quadrilateral WXYZ!

A. parallelogram

B. quadrilateral

C. rectangle

D. rhombus

2. Which type of quadrilateral hastwopairs ofcongruent, adjacent sides?

A. only a kite

B. onlya parallelogram

C. onlya trapezoid

D. a kite or a trapezoid

3. Which statementbelow isalways true?

A. Every rhombus is also a square.

B. Every square is also a rhombus.

C. Every kite is also a trapezoid.

D. Every trapezoid is also a kite.

156

JZglmigW>>2i£&^>&>£tngMx&Y&^

4. Lorraine drewa quadrilateral with tworightangles, one obtuse angle, and oneacute angle. What type of quadrilateraldid she draw?

A. kite

B. parallelogram

C. rectangle

D. trapezoid

5. Which of the following terms CANNOT beused to describe quadrilateralJKLM\

A. trapezoid

B. rectangle

C. rhombus

D. square

6. Which statement below is false?

A. Some parallelograms arealso squares.

B. Some parallelograms are alsotrapezoids.

C. Every rectangle isalso a parallelogram.

D. Every rhombus is also a parallelogram.

Duplicating any part of this bookis prohibited by law.

^^r=~r^r£^ssoni24^pectai^adnlaterals

7. The parallelogram hierarchy is represented in theVenn diagram below. One element ismissing fromthe diagram.

parallelogram

rectangle J( rhombus r^^^^

Which is the missing element?

A. circle

B. cube

C. square

D. triangle

8. Finndrewquadrilateral PQRS, so that bothpairs of opposite sides are parallel. Whichcould NOT be the figure that Finn drew?

A. square

B. rectangle

C. rhombus

D. trapezoid

Duplicating any part ofthis bookis prohibited by law.

9. Which statement below is false?

A. Every kite isa quadrilateral.

B. Every square is a quadrilateral.

C. Some trapezoids arealso rectangles.

D. Some rectangles arealso rhombi.

157g

Lesson Practice

Choose the correct answer.

1. What is the length of ABwith endpointsA(-2, 3) and 5(1, 2)?

y

-6 -5 -4 -3 -2 -1 0-1

-2

-3

-4

-5

-6

A. V2 units

B. 2 units

C. VTO units

D. 10 units

8

12 3 4 5 6*-X

2. What is the distance between point Z at(2, 5) and;/ = ~5x + 1?

162

A. 4IL unitsVTo

B. ^ unitsV5

+-x

C. -p= unitsVTO

D. 1 unit

tmm —lit

^^J/

3. What is the midpointbetween these twopoints: (-1, -3) and (7, -13)?

A. (-3,-8)

B. (3,-8)

C. (3,8)

D. (8,-3)

4. On the map ofAlphaville below, TownHall isat the origin (0, 0). Allen lives 3blocks east and 2 blocks north ofTown

Hall. Bartholomew lives 11 blocks east

and 8 blocks north ofTown Hall. Allen

and Bartholomew plan to meetexacdyhalfway between their houses. What arethe coordinates of the location where theyshould meet?

Town

West-*

South

A. (5,7)

B. (6,5)

C. (7,4)

D. (7,5)

artholomew's[House

*-xEast

Duplicating any partofthisbook is prohibited by law.}4

Lesson 26: triangles and Quadrilaterals in the Coordinate Plane

Lesson PracticeX^J^S^M^^^!^^^^^ •/jhUgjttY&t. J^MM\\ClWjlW£irjXVO;i VHiX.-j 11 WjMjUf.-J (uVUJ. i^i?ijifc^!JiHjriLlti^^^;J.IIJAlLV. LV.-

Choose the correct answer.

Quadrilateral ABCD below is a rectangle.Use this figure for questions 1 and 2.

1.

2.

Jt

1B

A

6-sV»-3-2-10-1

-2

-3

-4

! i '1 !> <

c

c< '

*-x

Which statement below is true and could be

used to help prove that quadrilateral ABCDisa rectangle?

A. Opposite sides ofa rectangle arecongruent, and AB = BC = 5 units.

Opposite sides of a rectangle arecongruent, and AB = DC = 5 units.

Opposite sides of a rectangle arecongruent, and AD = BC = 8 units.

D. All four sides of a rectangle arecongruent, andAB = BC= CD = AD.

Theperimeter of a rectangle is found usingthis formula: P —2(1 + w), whereP = perimeter, / = length, and w = width.What is the perimeter of rectangle ABCD1

A. 24 units

B. 25 units

C. 26 units

D. 30 units

B.

C.

Duplicating any part of this book is prohibited by law.

—»aM«w.»..^a.a«.».

3. Add the lengths of the sides of ARSTto findits perimeter. What is its perimeter?

y

*-x

i .

^ 2 -7-1--xSy

-8-5-4-1 -2^/TO 1 2 3456

^2-7 -3

' '

A. 11+ VoT units

B. 10 + VoT units

C. 11+V22 units

D. 18 units

4. Which accurately describes AMNPbelow?

y

7 y/

-16-5-V J-2-1 0-t

-2

:! I 'i iL II

PJ A

A. equilateral triangle with all sides10 units long

B. equilateral triangle with all sides12 units long

C. isosceles triangle with sides measuring10 units, 10 units, and 12 units

D. isosceles triangle with sides measuring10 units, 12 units, and 12 units

167

Lesson Practice

Choose the correct answer.

1. Which of the following is the contrapositiveof the conditional statement below?

If a quadrilateral hasall four sidescongruent, then it isa rhombus.

A. If a quadrilateral has all foursidescongruent, then it isNOT a rhombus.

B. If a quadrilateral does NOT have allfour sides congruent, then it isNOT arhombus.

C. If a quadrilateral isa rhombus, then ithas all four sides congruent.

D. If a quadrilateral isNOT a rhombus,then it does NOT have all four sides

congruent.

2. Whichof the following is the converse ofthe conditional statement below?

If a person is a mathematics teacher, thenhe or she loves to solve problems.

A. If a person loves to solve problems,then he or she is a mathematics teacher.

B. If a person is NOT a mathematicsteacher, then he or she does NOT love

to solve problems.

C. If a person does NOT love to solveproblems, then he or she is NOT amathematics teacher.

D. If a person does NOT love tosolve problems, then he or she is amathematics teacher.

170

M^^IAIijIl^jl&JlJIjjjjJJjiLjr^^

3. Which of the following is the inverse of theconditional statement below?

If Leah earned 100% on the test, then

she received an A.

A. If Leah earned 100% on the test, then

she did NOT receive an A.

B. If Leah did NOT earn 100% on the

test, then she did NOT receive an A.

C. IfLeah did NOT receive an A, then she

did NOT earn 100% on the test.

D. If Leah received an A, then she earned

100% on the test.

4. The conditional statement below is true.

Ifa number is a natural number, then the

number isgreater than zero.

Determine the converse, inverse, and

contrapositive for this statement. Which ofthose statements is also true?

A. Only its converse is true.

B. Only its inverse is true.

C. Only its contrapositive is. true.

D. Its converse, inverse and contrapositiveare all true.

Duplicating any part of this bookis prohibited by law.3

5. What is the inverse of this conditional

statement?

If apolygon is aregular polygon, then ithas all sides congruent.

A. If a polygon has all sides congruent,then it isa regular polygon.

B. If a polygon is NOT a regular polygon,then it does NOT have all sides

congruent.

C. If a polygon isa regular polygon, thenit does NOT have all sides congruent.

D. If a polygon does NOT have all sidescongruent, then it isNOT a regularpolygon.

6. The conditional statement below is true.

If a triangle has one right angle, then it isa righttriangle.

Determine the converse, inverse, and

contrapositive for this statement. Which ofthose statements is also true?

A. Only its converse is true.

B. Only its inverse is true.

C. Only its contrapositive is true.

D. Its converse, inverse and contrapositiveare all true.

'%aDuplicating any part of this book is prohibited by law.

littonai statements

7. What is the converse of this conditional

statement?

If Hector is in the school band, then heplays a musical instrument.

A. If Hector plays a musical instrument,then he is in the school band.

B. If Hector plays a musical instrument,then he is NOT in the school band.

C. If Hector does NOT play a musicalinstrument, then he is NOT in the

school band.

D. If Hector is NOT in the school band,then he does NOT play a musicalinstrument.

8. Assume that the conditional statement "if

p, then ^"is true. Which ofthe followingMUST also be true?

A. Its converse must be true.

B. Its inverse must be true.

C. Its contrapositive must be true.

D. Its inverse, contrapositive, and conversemust all be true.

~..~.,d

Lesson Practicei&%Ki*a'irt.T2.&:™ ^j^^jj^^^

Choose the correct answer.

1. Whichof the following pairs of coordinatesnames a point that follows the patternshown below?

-6-6-4-3-2-10-1

-2

A. (3,-2)

B. (3,-li)

C. (4,-li)

D. (4,-2)

3 4 5*-x

2. Monicamade this conjecture.

All prime numbers areodd.

Whichcounterexample couldbe used toshowthat the conjecture is false?

A. 2

B. 3

C. 4

D. 5

176

Ja<Aiiaa!»MHi«»iJMa»a«.M—» j^^jf&^iajg^l&iSi^ji!^

3. It is true that ifJaredarrives lateat his job,he will beput on probation. On Saturday,Jared arrived late at hisjob.Which of thefollowing isa valid conclusion?

A. Jaredwill need to work another shift.

B. Jared will be excused.

C. Jared will be put on probation.

D. Jared will NOT be put on probation.

4. Assume this statement is true.

If a figure is a square, then it is aquadrilateral.

According to the Law of Indirect Reasoning,if a figure isNOT a quadrilateral, whichconclusion can you draw?

A. Thefigure isa square.

B. Thefigure isNOT a square.

C. Thefigure isa rectangle, but NOT asquare.

D. The figure isa pentagon.

5. Tariq madethis conjecture.

If the productof twonumbers iseven,then the two numbers must be even.

Which counterexample could be used toshow that the conjecture is false?

A. 5-3=15

B. 4 • 15 = 60

C. -3 • (-5) = 15

D. 6-8 = 48

^Duplicating any part of this bookis prohibited by law.

^^^^^^^^^^^9^B^^3^^^ume^

6. Cathy is using three examples to prove this conjecture true:

The sum ofthe lengths oftwo sides ofa triangle is greater than the length ofthe third side.

3 + 4>5

3 + 5>4

4 + 5>3

Which isoneproblem with her reasoning?

A. The conjecture is not based on observations.

B. The conjecture is false.

C. The numbers in the examples are too small.

D. Her examples showonly right triangles.

7. Which of the following is NOT a valid argument?

A. If point B is the midpoint of AC, thenAB = BC.

B. If ABs CD, then CDm AB.

C. If AB = CD and CD = EF, then AB = EF.

D. If AB= CD and EF= GH, then AB= GH.

Duplicating any partof this book is prohibited by law.

2VF^1

2 + 2>2V2"

2 + 2V2"> 2

IttI•••-8l

Review

1. What is the midpoint of AB withendpointsy4(-l,0)andfl(5,2)?

*-x

A. (3,1)

B. (2,1)

C. (1,-2)

D. (-1,-3)

2. Which of the following is the contrapositiveof the conditional statement below?

If twoangles are congruent, then theyhave the same measure.

A. If two angles have thesame measure,then theyare congruent.

B. If two angles areNOT congruent, thenthey do NOT have the same measure.

C. If two angles do NOT have thesamemeasure, then they are NOTcongruent.

D. If twoangles do NOT have thesamemeasure, then they arecongruent.

178

3. Roselyn iscuttingfabric to make atriangular scarf. Which of the followingcould be the lengths of the three sides ofthe scarf?

A. 10 inches, 12 inches, 24 inches

B. 10 inches, 12 inches, 22 inches

C. 5 inches, 17 inches, 21 inches

D. 5 inches, 7 inches, 18 inches

4. What is the distance between point Rat(6, 3) and^ = 2x —6?

A. -£= units

B. -7= unitsV3

_ a

C. -^= unitsV3

D. -pr unitsV5

*-x

Duplicating any part of this book is prohibited by law. 1— • .-I --I —^ •** - •• -*

5. Point Z is the circumcenter of AJKL.l(KW= 5 inches, what is the lengthoffZ?

A Tl

->x^

1 4

A. 2.5 inches

B. 5 inches

C. 10 inches

D. 15 inches

6. What is the sum of the measures of the

interiorangles in a pentagon?

A. 900°

B. 540°

C. 360°

D. 108°

7. Which of the following isNOT a validargument?

A. If LA a LB, then LB = Z^4.

B. If LA = LB, and LB=LC, then^4 s lC.

C. I(LA= LB, and ilC = ^D, then

D. If LAand Z.5 form a linear pair, thenm^ + mLB = 180°.

I Duplicating any part of this bookis prohibited by law.

8. Whichof the following is the converse ofthe conditional statement below?

If a quadrilateral has four congruentsides, then it is a rhombus.

A. If a quadrilateral has four congruentsides, then it is NOT a rhombus.

B. If a quadrilateral does NOT have fourcongruentsides, then it is NOT arhombus.

C. If a quadrilateral is NOT a rhombus,then it does NOT have four congruentsides.

D. If a quadrilateral isa rhombus, then ithas fourcongruent sides.

9. In the diagram below, AD and BEbisecteach other.

Which can be used to prove AABC =ADEC>

A. SSS

B. ASA

C. SAS

D. AAS

1791

10. Below isa right triangle on a coordinategrid. The lengths of its legs are (x2 —#,)units and (y2 —_y,) units.

3I

i

x2.y2)-

i/ — i/v /2 /1

C-(x i, \ —-y — y —1*11/1/- —-a2 A,-

±tt It\ '

Which expression isequivalent to d, thelength of itshypotenuse?

A. (x2 - *,) + (y2 - .y,)

B. (x2 - xf + (y2 - yt)2

11. Which of the following isalways true?

A. Every parallelogram is also aquadrilateral.

B. Every kite isalso a parallelogram.

C. Every quadrilateral has four rightangles.

D. Every square is also a trapezoid.

180

12. In the diagram below, linesegments AD,BE, and CFaie angle bisectors of AABC.Which describes point G?

8

A. centroid

B. circumcenter

C. incenter

D. orthocenter

13. What is the distance between pointsr(-l,7)andV(-4,3)?

A. 4 units

B. 5 units

C. V29 units

D. V35 units

14. Francina made this conjecture.

For all real numbers x, the expression x2is greater than or equal to 1.

Which counterexample could be used toshow that the conjecture is false?

B. (1)2=1

C. (-3)2 = 9

D. (-8)2 = 64

1Duplicating any partof this book is prohibited by law.

OPEN-ENDED QUESTIONS

15. Triangle RSTbdow is a regular polygon, with exterior angle STVmeasuring 120°

S

T V

Chapter 4: Review

A. According to the Exterior-Angle Inequality Theorem, what doyou know about themeasures ofangles RSTand TRS without doing anycomputation?

B. Use the fact that ARSTis a regular polygon to find the measures ofinterior angles RSTandTRS. Show your work.

mLRST = degrees mZ. TRS = degrees

;; Duplicating any part of this book is prohibited by law. 181 iI*' • • -••• —•••- • -• •• •• • • •• • • - | .....J