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Practice BFor use with the lesson “Identify Symmetry“

Determine whether the figure has rotational symmetry. If so, describe the rotations that map the figure onto itself.

1. 2. 3. 4.

Does the figure have the rotational symmetry shown? If not, does the figure have any rotational symmetry?

5. 1208 6. 1808 7. 458

8. 368 9. 1808 10. 908

In Exercises 11–16, draw a figure for the description. If not possible, write not possible.

11. A triangle with exactly two lines 12. A quadrilateral with exactly two lines of symmetry of symmetry

13. A pentagon with exactly two lines 14. A hexagon with exactly two lines of symmetry of symmetry

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15. An octagon with exactly two lines 16. A quadrilateral with exactly four lines of symmetry of symmetry

17. Paper Folding A piece of paper is folded in half and some cuts are made, as shown. Which figure represents the piece of paper unfolded?

A. B. C. D.

In Exercises 18 and 19, use the following information.

Taj Mahal The Taj Mahal, located in India, was built between 1631 and 1653 by the emperor Shah Jahan as a monument to his wife. The floor map of the Taj Mahal is shown.

18. How many lines of symmetry does the floor map have?

19. Does the floor map have rotational symmetry? If so, describe a rotation that maps the pattern onto itself.

In Exercises 20 and 21, use the following information.

Drains Refer to the diagram below of a drain in a sink.

20. Does the drain have rotational symmetry? If so, describe the rotations that map the image onto itself.

21. Would your answer to Exercise 20 change if you disregard the shading of the figures? Explain your reasoning.

Practice B continuedFor use with the lesson “Identify Symmetry“

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3. (x, y) → (x 2 28, y 2 16)

4. (x, y) → (x 2 7n, y 2 4n)

5. (x, y) → (x 1 3, 2y) 6. (x, y) → (x 1 3, 2y)

7. (x, y) → (x 1 3, y 1 5)

8. (x, y) → (x 1 3, y 1 5)

9. (x, y) → (2x, 2y) 10. (x, y) → (y, 2x)

11. (x, y) → (x, y) 12. (x, y) → (x, y)

13. (x, y) → (y, x)

14. (x, y) → (2x 2 7, y 2 4)

15. (x, y) → (y, x 1 5)

16. (x, y) → (y, x 1 5)

17. (x, y) → (2y, 2x 1 5) 18. (x, y) → (2x, 2y)

19. (x, y) → (2x, y) 20. (x, y) → (2y, 2x 1 5)

21. RV 5 VR, RS 5 SR, U 4 5 V 2, S(UV) 5 (SU )V, and S(VU) 5 S(W(U3))22. Reflection in the x-axis 23. 3 Ï

}

65

24. Ï}

2a2 1 2b2 25. Ï}

2a2 1 2b2

26. Ï}}}}

2a2 1 2b2 2 4ab 2 6a 2 6b 1 65

27. Sample answer: j: x 5 0, k: x 5 3

28. Sample answer: j: y 5 2x, k: y 5 2x 1 5

29. Sample answer: j: y 5 2 a }

b x,

k: y 5 2 a }

b x 1

a2 1 b2

} 4

30. Sample answer: j: y 5 0, k: x 5 0

Lesson Identify SymmetryTeaching Guide

1. 1 2. no 3. 4 4. yes; 458, 908, 1358, or 1808 about the origin

Investigating Geometry Activity

1. a. b. c.

d. Sample answer:

2. a. yes b. no c. no d. yes

Practice Level A

1. 1 2. 0 3. 3 4. no 5. yes; a rotation of 1808 about its center 6. yes; a rotation of 908 or 1808 about its center

7. 1 line of symmetry; no rotational symmetry

8. 2 lines of symmetry; a rotation of 180° about its center

9. not possible 10. not possible

11. 12.

13. The figure has no rotational symmetry.

14. lines of symmetry: 1, rotational symmetry: no

15. lines of symmetry: 1, rotational symmetry: no

16. lines of symmetry: 1, rotational symmetry: no

17. lines of symmetry: no, rotational symmetry: yes, rotation of 180° about its center 18. 4 19. 4

20. yes; a rotation of 90° or 180° about its center

Practice Level B

1. yes; a rotation of 908 or 1808 about its center

2. yes; a rotation of 608, 1208, or 1808 about its center 3. yes; a rotation of 458, 908, 1358, or 1808 about its center 4. yes; a rotation of 458, 908, 1358, or 1808 about its center 5. yes 6. no; no

7. yes 8. no; yes, 408 9. yes 10. no; no

11. not possible

12. 13. not possible

14. 15.

Lesson Apply Compositions of Transformations, continued

GeometryChapter Resource Book A41

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16.

17. B 18. 4 19. Yes. The floor map can be ro-tated 908 or 1808 about its center.

20. Yes. The image can be mapped onto itself with a rotation of 1808 about its center.

21. Yes, the answer would change to a rotation of 908 or 1808 about its center. This is because the white figures can be mapped onto the shaded figures.

Practice Level C

1. yes; a rotation of 908 or 1808 about its center

2. yes; a rotation of 458, 908, 1358, or 1808 about its center 3. yes; a rotation of 458, 908, 1358, or 1808 about its center 4. yes; a rotation of 728 or 1448 about its center 5. yes 6. no; a rotation of 608, 1208, or 1808 about its center 7. yes

8. no; a rotation of 1808 about its center

9. no; 908 or 1808 about its center 10. no; a rotation of 1808 about its center 11. not possible

12. 13.

14. 15.

16. not possible

17.

18. b, d, p, q 19. The letters c, i, v, and w have one line of symmetry; the letters l, o, and x have two lines of symmetry. 20. l, o, s, x, z 21. 908

22. 368 23. 458

Study Guide

1. 5 2. 1 3. 6 4. yes; 458, 908, 1358, or 1808 about the center 5. no 6. yes; 1808 about the center

Interdisciplinary Application

1. center line

2. A cut made into the folded edge of the paper will create a design with four lines of symmetry.

3. Answers will vary. 4. 8 lines of symmetry

5. 22.58

Challenge Practice

1.

3 lines of symmetry; rotational: 1208 about the center

2. no lines of symmetry; no angles of rotation

3. Sample answer: Shade the three innermost parallelograms. 4. Sample answer: Shade two parallelograms reflected through the axis of symmetry not cut by the line of symmetry and then shade the parallelogram cut by the line of symmetry.

5. 4; Sample answer: Shade all the triangles except two of an isosceles trapezoid. The line of symmetry connects the base of the isosceles trapezoid without shaded triangles to the base of the opposite isosceles trapezoid; No

6. The figure with all of the triangles shaded has 6 lines of symmetry. 7. no 8. 208 9. about 8.68

10. 108 11. Yes; 458; Yes; 1208 12. 4208

Lesson Identify and Perform DilationsTeaching Guide

A9 B9 C9 D9

1. F 22 4 4 22 6 6 2 2G

Lesson Identify Symmetry, continued

GeometryChapter Resource BookA42

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