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Shape: Equiangular

Meaning

The term equiangular indicates that, in some figure, the angles are equal. It can be used to describe polygons, such as an equiangular pentagon. Image:EquiangularPentagon.png

The fact that the angles of a figure are congruent does not automatically mean that the sides are.

An equiangular (but not regular) hexagon: Image:EquiangularHexagon.png

Two equiangular octagons, one regular, one not: Image:EquiangularOctagon1.png Image:EquiangularOctagon2.png

If a quadrilateral is equiangular, it is a rectangle.

Mathematical background

In the case of triangles, being equiangular requires that the triangle also be equilateral. That is, every equiangular triangle is a regular triangle. However, this is not the case for all polygons. For example, a rectangle is equiangular -- all four angles are 90° -- but need not be square (need not have all four sides the same length). Thus, not all equiangular quadrilaterals are equilateral and so are not all regular.

Etymology

The prefix equi- is from Latin and means 'equal'.

Related mathematical terms

Equilateral, Regular, Rectangle