Video: Determining Whether a Given Shape Has Rotational Symmetry and Finding the Angle of Rotation If It Exists

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

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Video Transcript

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

If a figure has rotational symmetry — imagine holding the shape down of the center, like a pivot point. And if the shape can turn, less than a full turn all the way back to the start, so if it can turn less than that and it looked the same or looked unchanged, it has rotational symmetry. And that shape does.

Actually the turn that we’ve already drawn works. So here would be one example of rotational symmetry. Here is a second, turning it upside down. Here is a third. And if we were to draw a fourth one, it would be turning it all the way around a full 360 degrees back to the beginning.

So we need to find the angle of rotation. An entire rotation all the way around is 360 degrees. And from our picture, we can see that it takes four different turns to get all the way back around.

So in order to find the angle of rotation, we need to take 360 and divide by four. And we get 90 degrees. So this angle would be 90 degrees, and this one, and this one, and this one, making a full 360-degree circle.

So does our figure have rotational symmetry? Yes, and the angle of rotation is 90 degrees.

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