Question Video: Determining Whether a Given Shape Has Rotational Symmetry | Nagwa Question Video: Determining Whether a Given Shape Has Rotational Symmetry | Nagwa

# Question Video: Determining Whether a Given Shape Has Rotational Symmetry Mathematics

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

02:15

### Video Transcript

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

Because we’re thinking about rotational symmetry, that means we’re thinking about symmetry, if any, when we turn or rotate a shape. We can say that a shape has rotational symmetry if it appears unchanged after a rotation by an angle whose measure is strictly between zero degrees and 360 degrees. The two exact angles of zero degrees and 360 degrees are excluded as that would represent the original starting position.

Sometimes, if we find rotation difficult to visualize, it can be useful to use tracing paper. So, let’s say that we took some tracing paper and traced the shape and then began to rotate this tracing paper around in a clockwise direction. Is there any point other than at the starting point that this shape would look the same as it originally did? After 180 degrees, for example, the shape would look like this. We can say that it looks unchanged as this image looks like it’s upside down in comparison to the original shape.

The only time this shape appears unchanged is when we’ve rotated it through 360 degrees. But if we look at the definition again for rotational symmetry, we can’t include the occasion of 360 degrees. Therefore, we can give our answer to the first question that no, this figure does not have rotational symmetry.

We can also consider the order of rotational symmetry here. The order of rotational symmetry refers to how many times a shape looks like itself through a rotation of 360 degrees. Any shape that does not have rotational symmetry will have an order of rotational symmetry of order one.

Because this shape did not have rotational symmetry, we don’t need to find the angle of rotation. But we can do this using the order of rotational symmetry. We could use the formula that the angle of rotation is equal to 360 degrees divided by the order of rotational symmetry. But here we can give the answer as no, as the figure does not have rotational symmetry .

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