Name———————————————————————— Lesson
9.6
Date —————————————
Practice B
For 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?
6. 1808
8. 368
Lesson 9.6
7. 458
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
9-78
Geometry
Chapter Resource Book
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
5. 1208
Name———————————————————————— Lesson
9.6
Date —————————————
Practice B continued
For use with the lesson “Identify Symmetry“
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.
18. How many lines of symmetry does the floor
map have?
19. Does the floor map have rotational symmetry?
Lesson 9.6
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
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.
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.
Geometry
Chapter Resource Book
9-79
Lesson 9.5 Apply Compositions
of Transformations, continued
7. 1 line of symmetry; no rotational symmetry
3. (x, y) → (x 2 28, y 2 16)
answers
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. 2 lines of symmetry; 8. (x, y) → (x 1 3, y 1 5)
a rotation of 180°
about its center
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)
9. not possible 10. not possible
15. (x, y) → (y, x 1 5)
11.
16. (x, y) → (y, x 1 5)
12.
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,
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
S(UV) 5 (SU )V, and S(VU) 5 S (W (U 3))
}
22. Reflection in the x-axis 23. 3​Ï 65 ​ 
}
}
24. Ï
​ 2a 2 1 2b2 ​ 
25. Ï
​ 2a 2 1 2b2 ​ 
}}}}
26. Ï
​ 2a 2 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
a
29. Sample answer: j: y 5 2​ }  ​ x,
b
a
a2 1 b 2
​  4   
 
​
k: y 5 2​ }b ​  x 1 }
30. Sample answer: j: y 5 0, k: x 5 0
Lesson 9.6 Identify Symmetry
Teaching 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:
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
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
14.
15.
about its center
Geometry
Chapter Resource Book
A41
Lesson 9.6 Identify Symmetry,
continued
answers
16.
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
center line
1.
17. B 18. 4 19. Yes. The floor map can be rotated 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.
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.
Practice Level C
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.
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 9.7 Identify and
Perform Dilations
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
A42
Geometry
Chapter Resource Book
Teaching Guide
F
A9 B9 C9 D9
2 4 4 22
2
1.
6 6 2 2
G
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1. yes; a rotation of 908 or 1808 about its center