Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching...
-
Upload
ella-ramsey -
Category
Documents
-
view
235 -
download
0
description
Transcript of Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching...
![Page 1: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/1.jpg)
Unit #1 Scale Factor
![Page 2: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/2.jpg)
Matching sides of two or more polygons are called corresponding sidesMatching angles are called corresponding angles.
![Page 3: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/3.jpg)
Similar FiguresTwo figures are similar if• the measures of the corresponding angles are equal• the ratios of the lengths of the corresponding sides are proportional
Similar figures have the same shape but not necessarily the same size.
![Page 4: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/4.jpg)
Finding missing angles
• Hint: Remember angles are the same in corresponding angles!
What is angle D? <D
![Page 5: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/5.jpg)
Finding Missing lengths
111 y
___ 100 200
____ = Write a proportion using corresponding side lengths.
The cross products are equal.200 • 111 = 100 • y
The two triangles are similar. Find the missing length y
![Page 6: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/6.jpg)
y is multiplied by 100.22,200 = 100y
22,200 100
______ 100y 100
____ = Divide both sides by 100 to undo the multiplication.
222 mm = y
![Page 7: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/7.jpg)
Indirect Measurement
Indirect Measurement uses similar figures and proportions to find height of objects you cannot
measure directly
![Page 8: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/8.jpg)
Word Problems 1. Underline the question2. Set up your answer3. Draw it out 4. Find the similar shapes in your
drawing (triangles) 5. Use similar figures and proportions
to solve your problem!!!!
![Page 9: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/9.jpg)
A tree casts a shadow that is 7 ft. lawn. Ken, who is 6 ft tall, is standing next to the tree.
Kens has a 2-foot long shadow. How tall is the tree?
Step 1: underline the questionStep 2: Set up your answer: The tree is __________tall.
![Page 10: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/10.jpg)
Step 3: Draw it out
Step 4: Find the triangles
![Page 11: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/11.jpg)
2 7
__ 6 h
__ =
h • 2 = 6 • 7 2h = 42 2h 2
___ 42 2
___ =
h = 21
Write a proportion using corresponding sides.
The cross products are equal.
h is multiplied by 2.
Divide both sides by 2 to undo multiplication.
The tree is 21 feet tall.
Step 5: Proportions
![Page 12: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/12.jpg)
Example #2 Rockets
![Page 13: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/13.jpg)
A rocket casts a shadow that is 91.5 feet long. A 4-foot
model rocket casts a shadow that is 3 feet long. How tall is
the rocket?
Step 1: underline the questionStep 2: Set up your answer: The Rocket is __________tall.
![Page 14: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/14.jpg)
Step 3: Draw it out Step 4: Find the triangles
![Page 15: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/15.jpg)
91.5 3
____ h 4
__ =
4 • 91.5 = h • 3 366 = 3h
366 3
___ 3h 3
___ =
122 = h
Write a proportion using corresponding sides.
The cross products are equal.
h is multiplied by 3.Divide both sides by 3 to undo multiplication.
The rocket is 122 feet tall.
Step 5: Proportio
ns
![Page 16: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/16.jpg)
The map shown is a scale drawing. A scale drawing is a drawing of a real object that is proportionally smaller or larger than the real object. In other words, measurements on a scale drawing are in proportion to the measurements of the real object.
SCALE
![Page 17: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/17.jpg)
Is it set up right?Why or why not?
1. The scale on the map is 3 cm: 10 m. On the map the distance between two cities is 40 cm. What is the actual distance?
2. The scale on the map is 10 in: 50. On the map the distance between two schools is 30 in. What is the actual distance?
3 1040 x
10 3050 x
NO
Yes
![Page 18: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/18.jpg)
The scale on a map is 4 in: 1 mi. On the map, the distance between two towns is 20 in. What is the actual
distance? 20 in. x mi
_____ 4 in. 1 mi
____ =
1 • 20 = 4 • x 20 = 4x 20 4
___ 4x 4
___ = 5 = x
Write a proportion using the scale. Let x be the actual number of miles between the two towns.The cross products are equal.
x is multiplied by 4.
Divide both sides by 4 to undo multiplication.
5 miles
![Page 19: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/19.jpg)
Question #1 Find side GF
10 cm5 cm
7cm
6 cm
Answer: 12 cm
![Page 20: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/20.jpg)
Question #2 Determine if the ratios are proportional. Explain.
92 23121 34
No, cross proportions don’t equal (2783 doesn’t equal 3128)
![Page 21: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/21.jpg)
Question #3
You want to leave your server a 20% tip. The total bill
comes to $54.50. How much should you leave for a tip?
$10.90
![Page 22: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/22.jpg)
Question #4 A scale on a map reads 5 in: 50 miles. If two lakes
are 11 inches apart on the map, what is the actual
distance?
110 Miles
![Page 23: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/23.jpg)
Question #5 How do you know if
two figures are SIMILAR?
Angles are the EXACT SAME. Side lengths have to be proportionally similar
![Page 24: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/24.jpg)
Question #6 On a sunny afternoon, a
goalpost casts a 70 ft shadow. A 6 ft football player next to the goal post has a shadow 20 ft long. How tall is the
goalpost?
21 ft
![Page 25: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/25.jpg)
Question #7 If all angles are congruent, are
these two shapes SIMILAR
39
6
18Yes!
The cross products are equal! 54=54
OR 3/9 is equal to 6/18Scale Factor = 2
![Page 26: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/26.jpg)
Question #8
< A ___________
EF ___________
BA __________
<F ___________
![Page 27: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/27.jpg)
Answer
< A __<D_________
EF ____BC_______
BA ____ED______
<F ____<C_______
![Page 28: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/28.jpg)
Question #9 Is this a proportion?
2520
108
Yes!
The cross products are equal! 200=200
![Page 29: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/29.jpg)
Question #10
The following rectangles are similar. What is the length of
side RS?
![Page 30: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/30.jpg)
Question #11 A postcard is 6 inches wide and 14 inches long. When the postcard is
enlarged, it is 10 inches wide.
What is the length of the enlarged postcard?
![Page 31: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/31.jpg)
Unit #2 Measurement
![Page 32: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/32.jpg)
The customary system is the measurement system used in the
United States. It includes units of measurement for
length, weight, and capacity.
WHAT IS IT?
![Page 33: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/33.jpg)
What is a benchmark?
If you do not have an instrument, such as a ruler, scale, or measuring cup, you can estimate the length, weight, and capacity
of an object by using a benchmark. It helps you visualize actual
measurements!
![Page 34: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/34.jpg)
Customary Units of Length
Unit Abbreviation Benchmark
Inch in. Width of your thumb
Foot ft Distance from your elbow to your wrist
Yard yd Width of a classroom door
mile mi Total length of 18 football fields
Lengths
![Page 35: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/35.jpg)
What unit of measure would provide the best
estimate?A doorway is about 7_____________high
Feet
![Page 36: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/36.jpg)
Customary Units of WeightUnit Abbreviation Benchmark
Ounce oz A slice of breadPound lb A loaf of bread
Ton T A small car
Weight
![Page 37: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/37.jpg)
What unit of measure would provide the best
estimate?A bike could weigh 20 _____?
lb.
![Page 38: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/38.jpg)
CapacityCustomary Units of Capacity
Unit Abbreviation BenchmarkFluid ounce fl oz A spoonful
Cup c A glass of juicePint pt A small bottle of salad dressing
Quart qt A small container of paintGallon gal A large container of milk
![Page 39: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/39.jpg)
What unit of measure would provide the best
estimate?A large water cooler holds about
10 _____ of water.
Gallons
![Page 40: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/40.jpg)
Customary Conversion Factors1 foot = 12 inches1 yard = 3 feet1 yard = 36 inches1 mile = 5,280 feet1 mile = 1,760 yards1 pound (lb) = 16 ounces (oz)1 Ton (T) = 2,000 pounds1 gallon = 4 quarts 1 quart= 2 pints1 pint = 2 cups1 cup = 8 fluid ounces (fl oz)
![Page 41: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/41.jpg)
To convert from one unit of
measurement to another unit of measurement,
use a proportion
Cool, we’ve been using this since November!
![Page 42: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/42.jpg)
Important! Same measurements in the numerator
And Same measurements in the denominator
inches inchesfeet feet
not feet inchesinches feet
![Page 43: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/43.jpg)
How many feet are in 3 miles?
1 35,280 ?mile miles
ft
5,280 3 15,840 115,840 feet
![Page 44: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/44.jpg)
A book weighs 60 ounces. How many pounds is this?
1 ?16 60poundounces ounces
1 60 60 163.75pound
![Page 45: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/45.jpg)
Metric System:
King Henry Doesn’t Usually Drink Chocolate Milk
Memorize this!
![Page 46: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/46.jpg)
Naming the Metric Units• Meter units measure Length
• Gram units measure mass or weight
• Liter units measure volume or capacity.
![Page 47: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/47.jpg)
LengthUnit Abbreviation Relation to a
meterBenchmark
Millimeter
mm .001 m Thickness of a dime
Centimeter
cm .01 m Width of a fingernail
Decimeter
dm .1m Width of a CD case
Meter m 1 m Width of a single bed
Kilometer Km 1,000 m Distance around a city block
![Page 48: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/48.jpg)
Mass Unit Abbreviatio
nRelation to a
gramBenchmark
Milligram mg .001 g Very small insect
Gram g 1 g Large paper clip
Kilogram kg 1,000 g Textbook
![Page 49: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/49.jpg)
Capacity
Unit Abbreviation
Relation to a liter
Benchmark
Milliliter
mL .001 L A drop of water
Liter L 1 L Blender Container
![Page 50: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/50.jpg)
Example #1:(1)Look at the problem. 56 cm = _____
mm
Look at the unit that has a number. 56 cm
On the device put your pencil on that unit. k h d U d c m
km hm dam m dm cm mm
![Page 51: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/51.jpg)
Example #1:
k h d U d c m
km hm dam m dm cm mm
2. Move to new unit, counting jumps and noticing the direction of the jump!
One jump to the right!
![Page 52: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/52.jpg)
Example #1:3. Move decimal in original number
the same # of spaces and in the same direction.
56 cm = _____ mm
56.0.
Move decimal one jump to the right. Add a zero as a placeholder.
One jump to the right!
![Page 53: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/53.jpg)
Example #1:
56 cm = _____ mm
56cm = 560 mm
![Page 54: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/54.jpg)
Question¼ lb=
________________oz
4
![Page 55: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/55.jpg)
Question8 cups =
________________fl oz
16
![Page 56: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/56.jpg)
Question346 yards=
________________inches
12,456 inches
![Page 57: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/57.jpg)
Question10 quarts =
________________gal
2.5
![Page 58: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/58.jpg)
QuestionAn average cat weighs
15__________(ounces, pounds, tons)
Pounds
![Page 59: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/59.jpg)
Question130 g = ________kg
.13 kg
![Page 60: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/60.jpg)
QuestionWhat would be a reasonable measurement for the
distance from NGMS to NGHSCustomary
Mile
![Page 61: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/61.jpg)
QuestionHow many pints are in a gallon?
8
![Page 62: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/62.jpg)
QuestionHow long is the line?
3.5 inches
![Page 63: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/63.jpg)
Unit #3 Symmetry
![Page 64: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/64.jpg)
A rotation is the movement of a figure around a point. A point of rotation can be on or outside a
figure.
The location and position of a figure can change with a rotation.
![Page 65: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/65.jpg)
A full turn is a 360° rotation. So a turn
is 90°, and a turnis 180°.
12__
14__
90°
180°
360°
![Page 66: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/66.jpg)
Clockwise CounterClockwise
![Page 67: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/67.jpg)
QuestionDraw a 180° counterclockwise rotation
![Page 68: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/68.jpg)
AnswerDraw a 180° counterclockwise rotation
![Page 69: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/69.jpg)
QuestionDraw a 90° counterclockwise rotation
![Page 70: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/70.jpg)
Answer
![Page 71: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/71.jpg)
Unit #3 2-D Figures
![Page 72: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/72.jpg)
• The area of a figure is the amount of surface
it covers. • We measure area in
square units.• Example: in , cm , etc.² ²
![Page 73: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/73.jpg)
6 cm
4 cm
A lw 224 6 4cm
Rectangles
![Page 74: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/74.jpg)
#1 Find the area of the figure
Write the formula.
Substitute 15 for l.
Substitute 9 for w.
A = lw
A = 15 • 9A = 135
The area is about 135 in2.
15 in.
9 in.
![Page 75: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/75.jpg)
![Page 76: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/76.jpg)
A parallelogram is a quadrilateral with opposite sides that are parallel.
![Page 77: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/77.jpg)
Base
Height
A=Bh
![Page 78: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/78.jpg)
Why does this work?
![Page 79: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/79.jpg)
9 cm
8 cm
4 cm
A bh 232 8 4cm
#1
![Page 80: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/80.jpg)
AREA OF A TRIANGLE
b
A = 12bh
The area A of a triangleis half the product of itsbase b and its height h.
h
Or A=bh÷2
![Page 81: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/81.jpg)
Find the area of the triangle.A = 12 bh Write the formula.
A = 12 (20 · 12) Substitute 20 for b and 12 for h.
A = 120The area is 120 ft2.
A = 12 (240) Multiply.
![Page 82: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/82.jpg)
AreaOf
Circles
![Page 83: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/83.jpg)
tttttttttttt
![Page 84: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/84.jpg)
Estimate the area of the circle. Use 3 to approximate pi.
A ≈ 3 • 202
A ≈ 1200 m2
19.7 m
A = r2 Write the formula for area.Replace with 3 and r with 20.
A ≈ 3 • 400 Use the order of operations.
Multiply.
![Page 85: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/85.jpg)
Estimate the area of the circle. Use 3 to approximate pi.
r = 28 ÷ 2
A ≈ 3 • 142
28 m
A = r2 Write the formula for area.
Replace with 3 and r with 14.
r = 14
Use the order of operations.
Divide.
r = d ÷ 2 The length of the radius is half the length of the diameter.
A ≈ 3 • 196A ≈ 588 m2 Multiply.
![Page 86: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/86.jpg)
5 ft
Question 1 Find the Area
17 ftAnswer:
85 ft²
![Page 87: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/87.jpg)
r = 20 ÷ 2
A ≈ 3 • 102
20 m
A = r2 Write the formula for area.
Replace with 3 and r with 10.
r = 10
Use the order of operations.
Divide.
r = d ÷ 2 The length of the radius is half the length of the diameter.
A ≈ 3 • 100A ≈ 300 m2 Multiply.
Question 2Find the Area
![Page 88: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/88.jpg)
Find the area of the triangle.A = 12 bh Write the formula.
A = 54The area is 54 in2.
A = 12 (108) Multiply.
24 ft
4 ft12
A = 12 (4 • 24)12
Substitute 4 for b and 24 for h.
12
Question 3Find the Area
![Page 89: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/89.jpg)
Unit #4 3-D Figures
![Page 90: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/90.jpg)
-A closed plane figure formed by three or more line segments that intersect only at their endpoints
![Page 91: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/91.jpg)
-A three dimensional figure in which all the surfaces are polygons
![Page 92: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/92.jpg)
-A flat surface (polygon) on a solid figure
![Page 93: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/93.jpg)
-The segment where two faces meet
![Page 94: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/94.jpg)
-The point where three or more edges meet
![Page 95: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/95.jpg)
BaseA side of a polygon; a face of a
three dimensional figure by which the figure is measured
or classified.
![Page 96: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/96.jpg)
PrismA polyhedron that has two congruent, polygon shaped bases and other faces that are all rectangles.
![Page 97: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/97.jpg)
Prism named after what kind of BASE it has
![Page 98: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/98.jpg)
PyramidA polyhedron with a polygon base and
triangular sides that all meet at a common vertex.
![Page 99: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/99.jpg)
Pyramid named after what kind of BASE it has
![Page 100: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/100.jpg)
CylinderA three dimensional figure with two parallel, congruent circular bases connected by a curved
lateral surface.
![Page 101: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/101.jpg)
ConeA three dimensional figure with one vertex and one circular base.
![Page 102: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/102.jpg)
CubeA rectangular prism with six congruent square
faces.
![Page 103: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/103.jpg)
Question
What is a 3-D shape that has 5
FACES
Pyramid
![Page 104: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/104.jpg)
Which of the nets below could be used to form a pyramid like the one below?
Question
![Page 105: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/105.jpg)
12 in²
12 in²
30 in²
WHAT IS THE
SURFACE AREA
Question
54 in²
![Page 106: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/106.jpg)
FORMULA SHEET
a=Bh Rectangular Prism: l x w
Cylinder Prism: π 𝒓 ²
![Page 107: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/107.jpg)
What is It?!?!• Volume- The number of cubic units needed to ____________ a
space
• Volume is measured in:
FILL
CUBIC UNITS
![Page 108: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/108.jpg)
The figure below is a net for a cube. Suppose the square labeled 3 is the bottom face of this cube. Which number names the square that will be the front face of the cube?
a. 1b. 2c. 5d. 6
![Page 109: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/109.jpg)
How many vertices does the rectangular prism have?
a. 4b. 6c. 8d. 10
![Page 110: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/110.jpg)
Find the volume of the cylinder.
a. 122.46 in3
b. 244.92 in3
c. 367.38 in3
d. 734.76 in3
![Page 111: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/111.jpg)
Find the volume of the cone.
a. 37.68 m3
b. 452.16 m3
c. 113.04 m3
d. 169.56 m3
![Page 112: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/112.jpg)
QuestionHow many 1 inch
cubes can fit in a box that is 5 inches wide, 2 inches tall and 10 inches long?
100 in³
![Page 113: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/113.jpg)
QuestionMatch each situation with the appropriate units of measure. a. 25.3 cm2 _______ volume of a rectangular prismb. 25 m __________ perimeter of a large squarec. 5 mm __________ area of a parallelogramd. 25.64 ft3 __________ length of a mosquito
da
Cb
![Page 114: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/114.jpg)
Find the Surface Area
72 in²
![Page 115: Unit #1 Scale Factor. Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.](https://reader035.fdocuments.in/reader035/viewer/2022081503/5a4d1b067f8b9ab05998891b/html5/thumbnails/115.jpg)
PRACTICE a. Top view b. Front view c. Right view