Rotation Symmetry
Bill Zahner
Lori Jordan
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Printed: June 17, 2016
AUTHORS
Bill Zahner
Lori Jordan
www.ck12.org
C HAPTER
Chapter 1. Rotation Symmetry
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Rotation Symmetry
Here you’ll learn how to determine whether or not a shape has rotation symmetry.
What if you were asked to consider the presence of symmetry in nature? The starfish, below, is one example of
symmetry in nature. Draw in the center of symmetry and the angle of rotation for this starfish. After completing this
Concept, you’ll be able to answer questions like these.
Watch This
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/137552
CK-12 Foundation: Chapter12RotationSymmetryA
Guidance
A figure exhibits rotational symmetry if it can be rotated (less than 360◦ ) and look the same as it did before the
rotation. The center of rotation is the point that the figure is rotated around such that the rotational symmetry holds.
Typically, the center of rotation is the center of the figure. Along with rotational symmetry and a center of rotation is
the angle of rotation that tells us how many degrees to rotate the figure so that it still looks the same. In general, if
◦
a shape can be rotated n times, the angle of rotation is 360
n . Multiply the angle of rotation by 1, 2, 3...n to find the
additional angles of rotation. The number of rotations may be referred to as the order.
Example A
Determine if the figure below has rotational symmetry. Find the angle of rotational symmetry and the order.
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A regular pentagon can be rotated 5 times to demonstrate rotational symmetry, so it is order 5. Because there are 5
◦
◦
lines of rotational symmetry, the angle would be 360
5 = 72 .
Example B
Determine if the figure below has rotational symmetry. Find the angle and how many times it can be rotated.
The N can be rotated twice, so it is order 2. The angle of rotation is 180◦ .
Example C
Determine if the figure below has rotational symmetry. Find the angle and how many times it can be rotated.
The checkerboard can be rotated 4 times. There are 4 lines of rotational symmetry, so the angle of rotation is
◦
360◦
◦
◦
◦
◦
◦
4 = 90 . It appears the same at 0 (or 360 ), 90 , 180 , and 270 .
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Chapter 1. Rotation Symmetry
Watch this video for help with the Examples above.
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/137553
CK-12 Foundation: Chapter12RotationSymmetryB
Concept Problem Revisited
The starfish has rotational symmetry of 72◦ . Therefore, the starfish can be rotated 72◦ , 144◦ , 216◦ , 288◦ , and 360◦
and it will still look the same. The center of rotation is the center of the starfish.
Guided Practice
Find the angle of rotation and the number of times each figure can rotate.
1.
2.
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3.
Answers:
1. The parallelogram can be rotated twice, so it is order 2. The angle of rotation is 180◦ .
2. The hexagon can be rotated six times, order 6. The angle of rotation is 60◦ .
3. This figure can be rotated four times, order 4. The angle of rotation is 90◦ .
Explore More
1.
2.
3.
4.
5.
If a figure has 3 lines of rotational symmetry, it can be rotated _______ times.
If a figure can be rotated 6 times, it has _______ lines of rotational symmetry.
If a figure can be rotated n times, it has _______ lines of rotational symmetry.
To find the angle of rotation, divide 360◦ by the total number of _____________.
Every square has an angle of rotation of _________.
Determine whether each statement is true or false.
6. Every parallelogram has rotational symmetry.
7. Every figure that has line symmetry also has rotational symmetry.
Determine whether the words below have rotation symmetry.
8.
9.
10.
11.
12.
OHIO
MOW
WOW
KICK
pod
Find the angle of rotation and the number of times each figure can rotate.
13.
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Chapter 1. Rotation Symmetry
14.
15.
Determine if the figures below have rotation symmetry. Identify the angle of rotation.
16.
17.
18.
Answers for Explore More Problems
To view the Explore More answers, open this PDF file and look for section 12.2.
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