What exactly is rotational symmetry, and how do you know a figure has it? If you rotate a figure less than 360° around a fixed central point, and the figure looks exactly the same, the figure has rotational symmetry. The point around which the figure is rotated is called the center of rotation. The smallest angle that you can turn the figure is called the angle of rotation.
Let's take a look at a few examples. Work through the following tabs below to learn more about rotational symmetry.
Example 1
Example 2
Example 3
The image above is of a square with four equal sides and four angles that measure 90°. Think about rotating this figure. What would be the angle of rotation? You may need to sketch the rotation of the square a few different ways. Here is a hint: What happens when the figure is rotated 45°? Is that enough? What about 90°?
This square can be rotated 90°, and it will look exactly the same as it did when it started. Please note that anything less than a 90° rotation will not make a symmetric figure.
The image above is a star with 5 points. What do you think is the angle of rotation for this figure?
The angle of rotation for this figure is 72°. Since there are 5 points, you take a full rotation of 360° and divide it by 5 to calculate an angle of rotation of 72°.
The image above is an equilateral triangle. What is the angle of rotation for this triangle. Think about your answer then click on the Show Me Button to check your work.
The angle of rotation for this triangle is 120°. Since the triangle has three vertices, you take a full 360° rotation and divide it by 3 to calculate an angle of rotation of 120°.
