Is a rhombus a regular polygon?

1 Answer
Emily
Mar 20, 2016

A rhombus is not a regular polygon.

Explanation:

A regular polygon must be both equiangular (all angle measures are the same) and equilateral (all side lengths are the same). A rhombus meets one of the requirements: it is equilateral. But, all of a rhombus's angles are not the same. It is not equiangular, so it is not a regular polygon.

Take the rhombus below. The hash marks tell us that all of its sides are equal. It it equilateral. However, all of its angle measures are not the same. Angles C and A are equal, while angle B and D are equal. It has two sets of equal angles, but all of its angles are not equal. A is not equal to D. Therefore, it is not regular.
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