Yes, regular polygons have equal side lengths and equal interior angles as for example an equilateral triangle or maybe a square.
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True.
Regular shapes are both equilateral and equiangular. Irregular shapes may or may not be equilateral and equiangular.
They are both regular polygons.
A square would fit the given description
The terms equiangular means a polygon having the same angle between any two adjacent sides. Equilateral means all sides of equal length. A polygon can be equilateral without being equiangular (the rhombus) and equiangular without being equilateral (the rectangle). If a polygon is both equilateral and equiangular, it is a "regular polygon" such as the pentagon, square, and equilateral triangle.