Symmetry
9-4
Vocabulary
Review
1. Circle the center of rotation for the transformation at the right.
A
B
B
C
D
E
F
A
2. If S is the center of rotation of a figure that contains point Y,
then SY' 5
D
B’
.
C
C’
3. Cross out the figure(s) for which point A is NOT the center of rotation.
A
A
E
F
A’
A
symmetry (noun)
SIM
uh tree
Related Word: symmetrical (adjective)
Math Usage: A figure has symmetry if there is an isometry that maps the figure onto
itself. Figures having symmetry are symmetrical.
Use Your Vocabulary
4. Complete each statement with the appropriate form of the word symmetry.
NOUN
Some figures have rotational 9.
ADJECTIVE
A figure that maps onto itself is 9.
Underline the correct word to complete each sentence.
5. A figure that is its own image is symmetrical / symmetry .
6. A line of reflection is a line of symmetrical / symmetry .
7. A butterfly’s wings are symmetrical / symmetry .
Chapter 9
234
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
Vocabulary Builder
Key Concept Types of Symmetry
A figure has line symmetry or reflectional symmetry if there is
a reflection for which the figure is its own image. The line of
reflection is called a line of symmetry. It divides the figure into
congruent halves.
8. Does the trapezoid at the right have a horizontal line of symmetry?
Yes / No
A figure has rotational symmetry if there is a rotation of 180° or less
for which the figure is its own image. The angle of rotation for rotational
symmetry is the smallest angle needed for the figure to rotate onto itself.
9. Is the measure of the angle of rotation for an equilateral triangle 60°?
120
Yes / No
A figure with 180° rotational symmetry also has point symmetry. Each
segment joining a point and its 180° rotation image passes through the
center of rotation.
180
A square, which has both 90° and 180° rotational symmetry, also has
point symmetry.
10. Is the center of rotation of the parallelogram at the right equidistant
from all vertices?
Yes / No
Problem 1 Identifying Lines of Symmetry
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
Got It? Draw a rectangle that is not a square. How many lines of symmetry does
your rectangle have?
11. Circle the figure that is a rectangle but not a square.
12. Draw a rectangle that is not a square on the grid at the right.
13. Lines of symmetry divide a figure into
congruent parts.
14. Draw the line(s) of symmetry on your rectangle.
15. Does your rectangle have a vertical line of symmetry?
Yes / No
16. Does your rectangle have a horizontal line of symmetry?
Yes / No
17. Does your rectangle have a diagonal line of symmetry?
Yes / No
18. A rectangle that is not a square has
line(s) of symmetry.
235
Lesson 9-4
Problem 2
Identifying a Rotational Symmetry
Got It? Does the figure at the right have rotational symmetry? If so,
what is the angle of rotation?
19. Underline the correct word to complete the sentence.
Each / No side is horizontal or vertical.
20. To keep the same orientation of the sides, the angle of rotation must be
8.
a multiple of
21. Draw the image after a 908 rotation
about point P. Two sides are drawn
for you.
22. Draw the figure after a 1808 rotation
about point P. Two sides are drawn
for you.
P
P
23. Does the figure have rotational symmetry? If so, what is the angle of rotation?
_______________________________________________________________________
Identifying Symmetry in a Three-Dimensional Object
Got It? Does the lampshade have reflectional symmetry in a plane,
rotational symmetry about a line, or both?
Write T for true or F for false.
24. A plane that is parallel to the top of the lampshade and passes
through its middle divides the lampshade into two congruent parts.
25. A plane that is perpendicular to the top of the lampshade and passes
through its middle divides the lampshade into two congruent parts.
26. The lampshade can be rotated about a horizontal line so that it
matches perfectly.
27. The lampshade can be rotated about a vertical line so that it matches
perfectly.
28. Does the lampshade have reflectional symmetry in a plane, rotational symmetry
about a line, or both? Explain.
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
Chapter 9
236
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
Problem 3
Lesson Check • Do you UNDERSTAND?
Error Analysis Your friend thinks that the regular pentagon in the diagram at
the right has 10 lines of symmetry. Explain and correct your friend’s error.
29. Place a ✓ in the box if the response is correct. Place an ✗ if it is incorrect.
Each line of symmetry bisects an angle of the pentagon.
Each line of symmetry bisects a side of the pentagon.
Each line of symmetry is parallel to another line of symmetry.
The pentagon has 10 congruent angles.
The pentagon has 10 congruent sides.
The pentagon has 5 congruent angles.
The pentagon has 5 lines of symmetry.
30. Explain your friend’s error.
________________________________________________________________________
________________________________________________________________________
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
31. Use the regular pentagon below. Draw each line of symmetry in a different color.
Math Success
Check off the vocabulary words that you understand.
symmetry
line of symmetry
Rate how well you can identify symmetry in a figure.
Need to
review
0
2
4
6
8
Now I
get it!
10
237
Lesson 9-4