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Video: Determining Whether a Given Shape Has Rotational Symmetry

Bethani Gasparine

Does the following figure have rotational symmetry? If yes, find the angle of rotation.

02:06

Video Transcript

Does the following figure have rotational symmetry? If yes, find the angle of rotation.

A figure has rotational symmetry if it can be rotated or turned less than 360 degrees about its center so that the figure looks exactly as it does in its original position. So how do you rotate a figure? Imagine placing your finger at the center of this figure, and then turning it to see if there’s a place that you could turn to where it looked exactly the same as it did when you started. The degree measure of the angle through which the figure is rotated is called the angle of rotation. Basically, how far did you have to rotate it for it to look exactly the same as it did in its original position. That is measured in degrees.

Here would be the center of our figure. For reference, we’ll call this paddle number one, paddle number two, and paddle number three. We could rotate this figure about its center from paddle number one to paddle number two, and it would look exactly the same. We could also rotate from paddle number two to paddle number three and from paddle number three to paddle number one.

Since all of these rotations together would make an entire circle; that would be 360 degrees. And since all three rotations are equal, we could just take 360 and divide by three which gives us 120 degrees. This means the figure does have rotational symmetry because we were able to turn or rotate our figure, and it looked exactly the same as the original position when we would hold it down at its center. And each of these rotations would be 120 degrees.

So final answer: yes, 120 degrees.