Yes, by definition. If it not equilateral AND equiangular, then it is not regular.
Chat with our AI personalities
A regular polygon is any polygon that has sides which are the same length and angles whose measures are equal. An equilateral triangle (also equiangular triangle) is a regular polygon. Other isosceles triangles (equilateral triangles are isosceles, but they are an exception) and scalene triangles are not regular polygons. A side note: Only in a triangle is a polygon regular solely if it is equilateral. (Since an equilateral triangle is equiangular as well). This is NOT always true in other polygons, like quadrilaterals, where it can be equilateral but not necessarily equiangular (a rhombus) or equiangular but not equilateral (a rectangle).
Yes, a regular polygon is always equiangular.
A rectangle is not always equilateral, although it is always equiangular. A rhombus is not always equiangular, but is always equilateral. A square is both equilateral and equiangular.
The term regular polygon is almost always used to refer to a polygon that has equal interior angles and equal side lengths. In that light, the equiangular polygon and a regular polygon are the same thing.
Squares, rhombera, and equilateral triangles are always regular.