12.1. Exploring Symmetry http://www.ck12.org
Rotational Symmetry
Rotational Symmetry:When a figure can be rotated (less that 360◦) and it looks the same way it did before the
rotation.
Center of Rotation: The point at which 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, figures will have anangle of rotation. The angle of rotation,
tells us how many degrees we can rotate a figure so that it still looks the same.
Example 3:Determine if each figure below has rotational symmetry. If it does, determine the angle of rotation.
a)
b)
c)
Solution:
a) The regular pentagon can be rotated 5 times so that each vertex is at the top. This means the angle of rotation is
360 ◦
5 =^72
◦.
The pentagon can be rotated 72◦, 144 ◦, 216 ◦, and 288◦so that it still looks the same.
b) The “N′′can be rotated twice, 180◦, so that it still looks the same.