Asked by c
Do all regular polygons have point symmetry? Explain.
Yes, because all regular polygons have symmetry of order 2.
Yes, because all regular polygons have a center of rotation.
No, because all regular polygons do not have a line of reflection.
No, because all regular polygons do not have rotational symmetry of 180°.
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GPT-5 mini
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Answer: No, because all regular polygons do not have rotational symmetry of 180°.
Explanation: a regular n-gon is invariant under rotation by 360°/n. It has 180° (point) symmetry only when 180° is a multiple of 360°/n, i.e. when n is even. Odd n (e.g. equilateral triangle) do not have 180° rotational symmetry, so not all regular polygons have point symmetry.
Explanation: a regular n-gon is invariant under rotation by 360°/n. It has 180° (point) symmetry only when 180° is a multiple of 360°/n, i.e. when n is even. Odd n (e.g. equilateral triangle) do not have 180° rotational symmetry, so not all regular polygons have point symmetry.
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