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Name ____________________________________________ Date ____________ Class ____________

Additional PracticeStretching and Shrinking

Investigation 1

1. Refer to the rectangle at the right for the exercises below.

a. Give the length and width of a larger similar rectangle.

Explain your reasoning.

b. Give the length and width of a smaller similar rectangle. Explain your

reasoning.

c. Give the length and width of a rectangle that is not similar to this one.

Explain your reasoning.

4 cm

3 cm

000200010271960393_Unit3_Inv1-4_p055-079.qxd 11/21/15 4:13 PM Page 55

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Investigation 1

Name ____________________________________________ Date ____________ Class ____________

Additional Practice (continued)

Stretching and Shrinking

2. Figure VWXYZ is an enlargement of figure ABCDE. Name all the pairs of

corresponding sides and all the pairs of corresponding angles of the two

figures.

3. a. Draw a square. Then draw a square with a side length that is twice the side

length of the original square. How many copies of the smaller square will

fit inside the larger square?

b. Will you get the same answer for part (a) no matter what side length you

choose for the original square? Explain your reasoning.

A

Y

X

W

V

Z

B

CD

E


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d.Investigation 1

4. a. Carl made shape B by making a photocopy of

shape A. What percent did he enter in the copier?

b. Amy made a photocopy of shape A by entering 250% into the photocopier.

Sketch the copy she got.

Shape A Shape B

Name ____________________________________________ Date ____________ Class ____________




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Name ____________________________________________ Date ____________ Class ____________

Additional Practice: Digital AssessmentsStretching and Shrinking

Investigation 1

5. Figure ABCDEF is similar to figure

UVWXYZ. Which of the following

statements are definitely true? Select all that apply.

D

E

F

C

A

B Y

X

W

V

U

Z

n Angle A corresponds to angle U.

n Angle C is congruent to angle W.

n Angle B corresponds to angle Y.

n Side DE corresponds to side XY.

n Side FE is the same length as side WX.

6. Which of the following are equivalent to 5 __ 8 ?

Select all that apply.

n 10

___ 16

n 7 ___

10

n 15

___ 24

n 0.625

n 0.0625

7. Use the tiles to show one way to find 30% of 92.

92

0.30

27.6

276

30

0.92

3

000200010271960393_PSA_Unit3_Inv1-4_p008-011.indd 58 14/12/15 4:30 PM

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d.Investigation 1

Name ____________________________________________ Date ____________ Class ____________

Skill: Using PercentStretching and Shrinking

Find the given percent of each number. Show your work.

1. 20% of 560 2. 42% of 200 3. 9% of 50

4. 40% of 70 5. 25% of 80 6. 50% of 80

7. 40% of 200 8. 5% of 80 9. 75% of 200

000200010271960393_Unit3_Inv1-4_p055-079.qxd 11/21/15 4:13 PM 9

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Name ____________________________________________ Date ____________ Class ____________


Investigation 2

1. Draw any rectangle that is not a square. Draw a similar rectangle by applying

a scale factor of 3 to the original rectangle.

a. How many copies of the original rectangle will fit inside the new rectangle?

b. Will you get the same answer for part (a) no matter what rectangle you use

as the original rectangle?

000200010271960393_Unit3_Inv1-4_p055-079.qxd 11/21/15 4:13 PM 0

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d.Investigation 2

Name ____________________________________________ Date ____________ Class ____________



2. Make a figure by connecting the following sets of points on the coordinate grid:

Set 1: (8, 5), (8, 8), (0, 8), (0, 5), (8, 5) Set 2: (4, 6), (8, 2), (0, 2), (4, 6)

Set 3: (2, 6), (1, 6), (1, 7), (2, 7), (2, 6) Set 4: (6, 6), (7, 6), (7, 7), (6, 7), (6, 6)

a. Suppose you used the rule (6x, 6y) to transform this figure into a new

figure. How would the angles of the new figure compare with the angles of

the original? How would the side lengths compare? Would the new figure

be similar to the original? Explain.

b. Suppose you used the rule (3x�1, 3y�4) to transform the original figure

into a new figure. Would the new figure be similar to the original? Explain.


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Investigation 2

Name ____________________________________________ Date ____________ Class ____________



3. Recall that Zug Wump was made from Mug Wump using a scale factor of 2.

What is the scale factor from Zug to Mug? Explain.

4. a. Wendy drew a very large Wump using the rule (8x, 8y). She said that the

scale factor from Mug to her Wump was 8 and that the scale factor from

Zug to her Wump was 4. Do you agree with Wendy? Explain.

b. Wendy could not figure out the scale factor from Bug Wump to her new

large Wump. What is this scale factor? (Hint: Applying the rule (3x, 3y) to

Mug creates Bug.)


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Name ____________________________________________ Date ____________ Class ____________


Investigation 2

5. The original figure below is transformed

using the rule (x 2 1, 2y).

y

O 4

2

4

�2�4

�2

�4

x

Which of these points are vertices of the

new transformed figure? Select all that apply.

n (2, 0)

n (2, 21)

n (21, 24)

n (23, 0)

n (23, 21)

n (1, 0)

n (21, 4)

6. Write the letter for each pair of figures in the correct box.

A B DCA B DC

A B DCA B DC

Similar Figures Not Similar Figures


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Investigation 2

Name ____________________________________________ Date ____________ Class ____________

Skill: Similar FiguresStretching and Shrinking

Tell whether the triangles are similar.

1. 2. 3.

4. List the pairs of figures that appear to be similar.

a. b. c. d.

e. f. g. h.


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d.Investigation 2

For Exercises 5 and 6, graph quadrilateral ABCD. Then graph its imageA�B�C�D� with the given scale factor.

5. A(2, �2), B(3, 2), C(�3, 2), D(�2, �2); scale factor 2

6. A(6, 3), B(0, 6), C(�6, 2), D(�6, �5); scale factor 12

Name ____________________________________________ Date ____________ Class ____________

Skill: Similar Figures (continued)


O�4�6 4 6x

y

�2

�4

�6

�2 2

6

4

2

O�4�6 4 6x

y

�2

�4

�6

�2 2

6

4

2


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Investigation 2

Name ____________________________________________ Date ____________ Class ____________

Skill: Similar Figures (continued)


7. Quadrilateral A�B�C�D� is similar to quadrilateral ABCD. Find the scale factor

from ABCD to A�B�C�D�.

O�4�6 4 6x

y

�2

�4

�6

�2 2

6

4

2

A

D

B

B �

A�C �

D �

C


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Name ____________________________________________ Date ____________ Class ____________


Investigation 3

1. On the grid below, make a right triangle with legs of length 8 and 12.

a. Give the leg lengths of two smaller right triangles that are similar to the

one you drew and that have whole-number side lengths.

b. Copies of each smaller triangle can be put together to exactly match the

original triangle. How many of each smaller triangle does it take to match

the original?


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Investigation 3

Name ____________________________________________ Date ____________ Class ____________



2. In the grid below, each unit represents 1 centimeter. On the grid, make an

isosceles triangle with base and height both equal to 6 centimeters.

a. Can isosceles triangles with base and height equal to 2 centimeters be put

together to exactly match the shape of the original triangle? Is each smaller

triangle similar to the original?

b. Can isosceles triangles with base and height equal to 4 centimeters be put

together to exactly match the shape of the original triangle? Is each smaller

triangle similar to the original?


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d.Investigation 3

3. Find the missing side lengths in each pair of similar figures below.

a.

b.

4. For each pair of similar figures below, give the scale factor from figure A to

figure B.

a. b.

c.

A

B

A

B

A B

x

6 cm

2 cm 2 cm 4 cm 4 cm

8 cmx

3 cm 2 cm

Name ____________________________________________ Date ____________ Class ____________




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Investigation 3

Name ____________________________________________ Date ____________ Class ____________



5. a. The drawing below shows how a square foot and a square yard compare.

How many square feet are in a square yard? Explain your reasoning.

b. Are a square foot and a square yard similar? If so, what is the scale factor

from a square foot to a square yard? What is the scale factor from a square

yard to a square foot?

c. Compare a square inch with a square foot. What is the scale factor from a

square inch to a square foot?

d. How many square inches are in a square foot? Explain.

e. Compare a square inch with a square yard. What is the scale factor from a

square inch to a square yard?

f. How many square inches are in a square yard?

1 yd1 ft

1 ft

1 yd


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Name ____________________________________________ Date ____________ Class ____________


Investigation 1Investigation 3

6. The figures below are similar. Use the

values in the bank to label the missing side

lengths.

12 15 16.5 18 32.5 36

12.5

30

135

7. The two pentagons below are similar.

Complete the missing side lengths using the

values in the bank.

1 __ 3 in. 2 __

3 in. 4 __

3 in. 1 in. 2 in. 3 in. 4 in.

6 in.

2 in.

2 in.

1 in.

in.43

in.43

8. Triangle ABC is similar to triangle A9B9C9. Circle the numbers that make the statements true.

The scale factor from triangle ABC to

triangle A9B9C9 is

Q 2 4

1 __ 2

1 __ 4

U because the coordinates of

each vertex are multiplied by Q 2 4

1 __ 2

1 __ 4

U .y

O 2 31

1

2

3

4

�2�4

�1

�2

�3

A�

B�

C� C

A

B

x

9. Rectangle A is a transformation of rectangle B, scaled by a factor of 4.

How many copies of rectangle B can fit inside rectangle A?

~ 2 ~ 4 ~ 8 ~ 16


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Investigation 3

Name ____________________________________________ Date ____________ Class ____________

Skill: Similar PolygonsStretching and Shrinking

The pairs of figures below are similar. Find the value of each variable.

1. 2.

3. 4.

5. 6. 15

9

6x8

4

5

x

20

15

10 8

y

xx

20

6

14

24 18

16y

5 5

5 5

5

4 x

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d.Investigation 3

Name ____________________________________________ Date ____________ Class ____________

Skill: Fractions, Decimals, and PercentsStretching and Shrinking

Write three equivalent fractions for each fraction.

1. 2.

3. 4.

5. 6.

7. 8.

Write each fraction as a decimal and as a percent.

9. 10.

11. 12. 1720

1325

710

35

832

1545

812

1520

34

56

78

310


1. a. Rachel was working with the triangles below:

She wrote the fraction . What was she thinking about?

b. Next, she wrote the fraction while working with these two triangles:

Was she thinking in the same way or differently? Explain.

3 cm

9 cm18 cm

6 cm

13

12

2 cm

4 cm

4 cm 8 cm

74


Name ____________________________________________ Date ____________ Class ____________


Investigation 4


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d.Investigation 4

Name ____________________________________________ Date ____________ Class ____________



2. Below are several pairs of similar figures. In each, find the missing

measurement(s).

a.

b.

c.

2.5 cm

5 cm 6.495 cm4.33 cm e

d

1.5 cm

10 cm

2.5 cm

b 5 cm

c

3 cm

4 cm 7.5 cm

a


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Investigation 4

Name ____________________________________________ Date ____________ Class ____________



3. In each figure below, find the missing measurement.

a.

b.

1.96 cm25 cm

y

6.72 cm 7 cm

1.8 cm5 cm

3 cm2.4 cm

x


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Name ____________________________________________ Date ____________ Class ____________


Investigation 4

4. Using the values from the bank, find the

missing measurement.

5 cm 6 cm 10 cm 12 cm 18 cm

3 cm6 cm

5. Which statements about the figures are

true? Select all that apply.

2.4 cm1.2 cm 1.0 cm

3.0 cm1.6 cm

6.0 cm

2.0 cm

3.2 cm

A

E

F

G

HB

C

D

2.4 cm1.2 cm 1.0 cm

3.0 cm1.6 cm

6.0 cm

2.0 cm

3.2 cm

A

E

F

G

HB

C

D

n ABCD is similar to EFGH.

n Side AB is congruent to side EF.

n Side DC corresponds to side HG.

n The ratio of side AB to side AD is the

same as the ratio of side EF to side EH.

n The scale factor from ABCD to EFGH

is 2.

6. Jaqué wants to calculate the scale factor for the pair of similar figures. Explain how she can

determine the scale factor from the figure on the left to the figure on the right.

First, she must identify the Q congruent

equivalent

corresponding

identical

matching

U sides.

Because one side of length12 cm corresponds

to a side of length Q

12 cm

6 cm

3 cm

U , she divides 12 by Q

12

6

3

U .

The result shows that the scale factor is Q  4 3

2

1 __ 2

U .

6 cm

12 cm

3 cm

6 cm


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Investigation 4

Name ____________________________________________ Date ____________ Class ____________

Skill: Similarity and RatiosStretching and Shrinking

Tell whether each pair of polygons is similar. Explain why or why not.

1. 2.

3. 4.

5. 6. P

O

R

Q

T

S

V

U6

64

4

8

8

3

3

4

44

4

H I

JG

9

9

9

9

L M

NK

B

A C

223

F

D E

6 6 9 9

4

9

8

11

T

S U

3

2 23

3 23

W

XV

33

3 4

3

J K

L

M

I

5

5

5

5

8

N

O P

Q

R

CB

A D

12

8

H

G

E

F 4

6


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d.Investigation 4

Name ____________________________________________ Date ____________ Class ____________

Skill: Similarity and Ratios (continued)


Exercise 7–11 show pairs of similar polygons. Find the missing side lengths.

7. 8.

9. 10.

11.x

y

12

1627

15

912

18

15

15

30

y

xy

x

30

4215

12

18

x

36 36

12

12

24 yx

y12

74

6


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