equiangular polygon
A polygon^{} is equiangular if all of its interior angles^{} are congruent.
Common examples of equiangular polygons are rectangles^{} and regular polygons^{} such as equilateral triangles^{} and squares.
Let $T$ be a triangle^{} in Euclidean geometry^{}, hyperbolic geometry, or spherical geometry. Then the following are equivalent^{}:

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$T$ is equilateral;

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$T$ is equiangular;

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$T$ is regular^{}.
If $T$ is allowed to be a polygon that has more than three sides, then the above statement is no longer true in any of the indicated geometries^{}.
Below are some pictures of equiangular polygons drawn in Euclidean geometry that are not equilateral.
Title  equiangular polygon 

Canonical name  EquiangularPolygon 
Date of creation  20130322 17:12:43 
Last modified on  20130322 17:12:43 
Owner  Wkbj79 (1863) 
Last modified by  Wkbj79 (1863) 
Numerical id  10 
Author  Wkbj79 (1863) 
Entry type  Definition 
Classification  msc 5100 
Synonym  equiangular 
Related topic  BasicPolygon 