Video: Understanding Lines of Symmetry

True or false? Any figure that has rotational symmetry must also have line symmetry.

01:19

Video Transcript

True or false? Any figure that has rotational symmetry must also have line symmetry.

We need to consider rotational symmetry and line symmetry. If a shape looks the same after some rotation, it has rotational symmetry. If one-half of the image is a reflection of the other half, it has line symmetry. This sideways S has rotational symmetry. If you held it down at that pink dot and spun this S 180 degrees, the shape would look the same.

We need to consider if this shape could have line symmetry. If you folded the S in half here, the shape would not be the same on both sides. If we folded it in half, lengthwise, it would still not be the same shape on both sides. This S shape does not have line symmetry.

And that means the statement “any figure that has rotational symmetry must also have line symmetry” is false.

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