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Transcript
equiangular polygon∗ Wkbj79† 2013-03-21 23:08:09 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: • T is equilateral; • T is equiangular; • 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. ∗ hEquiangularPolygoni created: h2013-03-21i by: hWkbj79i version: h39535i Privacy setting: h1i hDefinitioni h51-00i † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. 1
