Equilateral

Equilateral describes a figure whose sides are all equal in length. The term is most often used for polygons, but it can apply to any shape defined by equal-length segments. A polygon that has equal sides is called equilateral; if it also has all angles equal, it is called regular. An equilateral polygon is not necessarily regular, except in the case of triangles where equality of sides forces equality of angles.

Equilateral triangles are the most familiar example. All three sides are the same length, and all interior angles measure 60 degrees, making the triangle both equilateral and equiangular. Known properties include a height equal to (sqrt(3)/2) times the side length, an area of (sqrt(3)/4) times the square of the side, and a perimeter equal to three times the side length. They have three axes of symmetry and a single center where medians, altitudes, angle bisectors, and perpendicular bisectors coincide.

For polygons with more than three sides, equilateral means only that all sides are equal in length. A quadrilateral that is equilateral is a rhombus; such shapes are not necessarily square, since their angles may differ. In higher polygons, equilateral figures can exist without being regular, and their angles can vary while side lengths remain equal. Areas and other measurements often depend on the specific angles and diagonals of the shape.

Etymology traces the term to Latin roots meaning equal and side. The combination equi- and lateral (related to sides) yields equilateral, reflecting the defining property of equal side lengths.