Equilateral polygon

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In geometry, an equilateral polygon is a polygon which has all sides of the same length.

For instance, an equilateral triangle is a triangle of equal edge lengths. All equilateral triangles are similar to each other, and have 60 degree internal angles.

Any equilateral quadrilateral is a rhombus, which includes the square.

An equilateral polygon which is cyclic (its vertices are on a circle) is a regular polygon. Not all equilateral polygons are convex: all equilateral polygons with more than four sides, such as the pentagon, can be concave.

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.

[edit] 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.