http://www.ck12.org Chapter 12. Rigid Transformations
Example B
Determine if the figure below has rotational symmetry. Find the angle and how many times it can be rotated.
TheNcan be rotated once. 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 3 times. There are 4 lines of rotational symmetry, so the angle of rotation is
360 ◦
4 =^90
◦. It can also be rotated 180◦and 270◦and it will still look the same.Watch this video for help with the Examples above.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter12RotationSymmetryB
Concept Problem Revisited
The starfish has rotational symmetry of 72◦. Therefore, the starfish can be rotated 72◦, 144 ◦, 216 ◦, and 288◦and it
will still look the same. The center of rotation is the center of the starfish.
Vocabulary
Rotational symmetryis present when a figure can be rotated (less than 360◦) such that it looks like it did before the
rotation. Thecenter of rotationis the point a figure is rotated around such that the rotational symmetry holds. The
angle of rotationthat tells us how many degrees we can rotate a 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.
Guided Practice
Find the angle of rotation and the number of times each figure can rotate.
Answers:
- The parallelogram can be rotated twice. The angle of rotation is 180◦.
- The hexagon can be rotated six times. The angle of rotation is 60◦.
- This figure can be rotated four times. The angle of rotation is 90◦.