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Describe the dilation that moves figure A onto figure B.

1.

A

1017

PB

2. A

35

OB

3.

A

30 10Q

B

The two figures are similar. Describe the transformation(s) that move figure A onto figure B.

4.

A

1212

P

B

5.

A

18

8

PB

6.

A16

20

P

Q

B

Copy the figure. Draw an example of the given similarity transformation of the figure with center O.

7. dilation 8. dilation then translation 9. dilation then rotation

O O

O

Figure B is the image of figure A under a transformation. Tell whether the transformation involves a dilation. If so, give the scale factor of the dilation.

10. A

1620

B

11.

A B30

20 10

12.

AB

2030

6 6

69

99

9

6

Practice BFor use with the lesson “Transformations and Similarity”

Name ——————————————————————— Date ————————————

6-19Geometry

Chapter Resource Book

Lesson

6.2

Less

on

6.2

CS10_CC_G_MECR710761_C6L02PB.indd 19 5/12/11 4:27:54 PM

Coordinates of the vertices of a preimage and image figure are given. Describe the transformations that move the first figure onto the second.

13. A(24, 2), B(2, 4), C(22, 5); P(28, 4), Q(4, 8), R(24, 10)

14. O(0, 0), M(0, 4), N(6, 0); O(0, 0), F(0, 10), G(15, 0)

15. O(0, 0), S(0, 2), T(5, 0); O(0, 0), X(0, 24), Y(210, 0)

16. A(28, 0), B(0, 210), O(0, 0); P(4, 0), Q(0, 5), O(0, 0)

17. J(216, 0), K(0, 220), O(0, 0); M(28, 0), N(0, 10), O(0, 0)

18. Crafts Gail cuts and glues similar shapes onto a wooden board as a crafts project. One design with similar shapes is shown at the right. Describe a combination of three transformations that can be used to move shape A onto shape B.

19. Computers Cameron uses graphics software to create the figure shown at the right. He wants the length of the smaller flower petals to be

3 } 5 of the length of the larger petals. Describe a combination

of transformations that can be used to move petal A onto petal B.

Circle B is the image of circle A under a transformation. Prove the circles are similar by finding a center and scale factor of a dilation that moves circle A onto circle B.

20. tangent 21. concentric

A

B

28

9

A

B

6 4

2030

A

45º Q

P B

A

OB

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Name ——————————————————————— Date ————————————

GeometryChapter Resource Book6-20

Les

so

n 6

.2

CS10_CC_G_MECR710761_C6L02PB.indd 20 5/12/11 4:27:54 PM

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Lesson Use Similar Polygons, continuedc. 60, 735 d. The ratio of the perimeters is equal to the scale factor. The ratio of the areas is equal

to the square of the scale factor. 3. 517

4. a. 3.12 in. b. 15 5. 3.2 6. Answers will vary. 7. a. 10.6 lb per person b. 42.4 lb; about 3.53 lb c. about 11 oranges d. Sample answer: No; Some families eat more fruits than others. The oranges could have been used in recipes.

Challenge Practice

1. 7 }

4 2. 21 cm 3. JK 5 35 cm, JL 5 36.75 cm,

RS 5 20 cm, ST 5 13 cm, RT 5 21 cm

4. Area of n JKL 5 385.875 cm2;

Area of n RST 5 126 cm2; 3.0625:1;

The scale factor of the areas is the square of the scale factor of the perimeters.

5. Sample answer: 40

13

13

13

1313

13

A B

C D

E F

G H

ABDC > CDFE > EFHG

6. Sample answer: A B

CD

E

n EBC , n ABD, n ABD , n ECD, n EBC , n ECD

7. Yes; Sample answer: The side lengths are given (or can be determined by addition); trapezoid ABGF , trapezoid ACDE; Scale factor of the side lengths of trapezoid ABGF to trapezoid ACDE is 1 : 2.

Lesson Relate Transformations and Similarity

Teaching Guide

1. Sample answer: Triangles A and H; Triangles B, C, F, G

2. Sample answer: Squares D and E

3. Sample answer: Triangles B, C, F, and G

4. Sample answer: The large quilt-block Z

5. Sample answer: Rotation then dilation

6. Sample answer: dilation then translation

Practice Level A

1. 2

2. 3/5

3. 1/3

4. no

5. no

6. yes

7. dilation with center (0, 0) and scale factor 2

8. dilation with center (0, 0) and scale factor 1 }

4

9. dilation with center (0, 0) and scale factor 3 }

4

10. Sample answer:

11. Sample answer:

12. Sample answer:

13. A’(2.5, 2.5), B’(2.5, 6.25), C’(6.25, 6.25), D’(6.25, 2.5)

14. A’(0, 0), B’(3, 0), and C’(2, 0)

15. 8 inches

16. 2

Practice Level C

1. 3 cm

2. 18 in.

3. 9 mm

4. scale factor 1.5

5. scale factor 2 }

3

6. scale factor 2 } 5

7. scale factor 4

8. true

9. true

GeometryChapter Resource BookA80

6.2