review – chapter 4 & 5 stretching & shrinking by: ms. d. kritikos

REVIEW – CHAPTER 4 & 5Stretching & Shrinking

By: Ms. D. Kritikos

Similar Figures

Polygons that have the same shape are similar. Similar figures must have:Corresponding angles that are congruentCorresponding sides that have SCALE FACTOR (ratio

of the lengths are proportional)

The triangles below are similar. Find the missing measurements.

a 3 8 b 16 24

2.75 11 c

a = _____ b = _____ c = _____

There are 2 different ways to solve this problem:

FIRST WAY, by using Scale Factor: Find 2 corresponding sides in similar figures where

both measurements are know.Divide the larger number by the smaller number.Find the corresponding side to the unknown

measurement; if the smaller number is known, multiply it by the scale factor. If the larger number is known, divide it by the scale factor.

To solve this problem by using scale factor:

1. Find the known corresponding side measurements in the first 2 triangles.

a 3 8 b 16 24

2.75 11 c

a = _____ b = _____ c = _____

2.75 and 11

2. Divide the larger number by the smaller number.

3. Find the corresponding side to a (8) and divide it by the scale factor of 4.

2

Continue to use scale factor to find b:

1. Since the scale factor is 4 between the first 2 triangles, we can find b by applying it to the corresponding side of b.

a 3 8 b 16 24

2.75 11 c

a = _____ b = _____ c = _____

3

2. Multiply 3 by the scale factor of 4 to find b.

2 12

Continue to use scale factor to find c:

a 3 8 b 16 24

2.75 11 c

a = _____ b = _____ c = _____

8 and 16

2 12

1. Find the known corresponding side measurements in the second and third triangles.

2. Divide the larger number by the smaller number.3. Find the corresponding side to c (11) and multiply it by the scale factor of 2.

22

To solve this problem by using proportions:

1. Find the known corresponding side measurements in the first 2 triangles.

a 3 8 b 16 24

2.75 11 c

a = _____ b = _____ c = _____

2.75 and 112. Find the corresponding side to a (8).

2

Continue solving this problem by using proportions:

3. Set up the proportion in one of these two formats:

a 3 8 b 16 24

2.75 11 c

a = _____ b = _____ c = _____

surementingSideMeaCorrespond


surementUnknownMeaTriangle

rementKnownMeasuTriangle

1#

1#OR


surementUnknownMeaTriangle


ementKnowMeasurTriangle 2#1#

Finish solving this problem by using proportions:

a 3 8 b 16 24

2.75 11 c

a = _____ b = _____ c = _____

8

1175.2

a 811

75.2 aCross multiply to solve

for missing side

11875.2 a00.2211 a

2a

a 11875.2a1100.22 a2

2

Finish solving this problem by using proportions:

a 3 8 b 16 24

2.75 11 c

a = _____ b = _____ c = _____

2416

8 b

c

11

16

8Set up Proportions to

solve for b and c, then cross multiply to solve for missing sides.

b 16248b16192

b12

11168 c1768 c

22c

2 12 22

An antique shop has a large dollhouse that is a model of a real house. Here are some of the

measurements:

1. What is the height of the building? (hint: 100 cm = 1 m)

Height Dollhouse Actual house

Window 5 cm 1 m

Building 80 cm

Find the SCALE FACTOR between known corresponding sides, then apply that information to find the actual building height.

205100 mcm 1616008020

16 m (1600 cm)

(100 cm)


measurements:

2. If the area of the living-room floor in the dollhouse is ¼ of a square meter, how much carpeting will be needed to cover the floor in the real house??


Window 5 cm 1 m

Building 80 cm

Apply SCALE FACTOR squared for area, then multiply by the amount of carpeting needed for the doll house.

22 10025.40020 m

16 m


measurements:

3. If the dollhouse has 12 windows, how many windows does the real house have?


Window 5 cm 1 m

Building 80 cm

124. If it takes 25 centimeters of molding to frame the door of the

dollhouse, how much molding is needed to frame the door of the real house?

mcm 51005002025

Complete the table below.

2

5

Rectangle Scale Factor

Short Side

Long Side

Perimeter Area

A 1 2 5

B 2

C 5

D ½

14 10

4 10 28 40

10 25 70 250

1 2.5 7 2.5

The area of rectangle C is how many times larger than the area

of rectangle B?

Scale factor squared is the difference between the area of 2 similar figures.

B 2

4

C 6

12

842 72126 9872

932

The perimeter of rectangle C is how many times larger than the

perimeter of rectangle B?Scale factor is the difference between the perimeter of 2

similar figures.

B 2

4

C 6

12

12)6(2)24(2 36)18(2)126(2

31236 3SF

Joan used a mirror to estimate the height of a flagpole. What is the

height of the flagpole?

5 ft flagpole 2 ft---|-----------------9 ft-----------------------

x

5

9

2 592 x

452 x ftx 5.22

Find all the triangles similar to Triangle A.

A B C D E

12

6 3 4 5

9 3 1 3 2

3

4

9

12

2

1

3

6 3

1

3

3

4

2

5

ONLY D

Any questions??? Ask any questions you may have now. That is the

purpose of a review. Today and tomorrow is for questions, not the day of the test.

Complete the review sheet individually. While in class, if you have a question, please ask your teacher. While finishing the review sheet at home, write down any questions you may have so you can ask them tomorrow.

Come to class tomorrow with the completed review sheet. We will discuss each question in class, and you will have the opportunity to ask questions.

review – chapter 4 & 5 stretching & shrinking by: ms. d. kritikos

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