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In geometry, an 'equilateral polygon ' is a polygon which has all sides of the same length.
An 'equilateral' polygon which is convex and cyclic (its vertices are on a circle) is a regular polygon.
An equilateral triangle is a triangle of equal edge lengths. All equilateral triangles are similar to each other with 60 degree angles.
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Any equilateral quadrilateral is a rhombus, these include the square.
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Any ''n''-sided polygon which has ''n'' sides of equal length can be considered an equilateral. Not all equilaterals are convex geometric shapes: consider that for a pentagon two adjacent sides can be reflected in the line segment joining the two extreme vertices.
Viviani's Theorem holds for equilateral polygons.
:''The sum of distances from a point to the side lines of an equilateral polygon does not depend on the point and is that polygon's invariant.''

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External links

External links

★ Equilateral triangle With interactive animation

★ A Property of Equiangular Polygons: What Is It About? a discussion of Viviani's theorem at Cut-the-knot.