inequilateral

Inequilateral is an adjective meaning not having equal sides. In geometry it is most often used to describe a triangle whose three sides have distinct lengths. In everyday use it can also be used for polygons that have no two sides of the same length, though for polygons other than triangles the term is far less common.

In triangles, inequilateral is effectively synonymous with scalene; a triangle with all sides of different lengths. By contrast, an equilateral triangle has all sides equal, and an isosceles triangle has exactly two equal sides. Because equal sides imply equal opposite angles, a true inequilateral (scalene) triangle has three unequal angles.

Properties: The side-length inequality does not constrain angle measures beyond the triangle angle sum of 180 degrees; in a scalene triangle, all three interior angles are distinct. The triangle inequality rules still apply (sum of any two sides exceeds the third). A 3-4-5 triangle is a common example of an inequilateral/scalene triangle.

Etymology and usage: The word comes from not equal (in- + equi-) + side or lateral. In formal mathematics, scalene is the standard term for a triangle with no equal sides, while inequilateral is used less often and may be encountered as a synonym. See also: Scalene triangle, Isosceles triangle, Equilateral triangle, Polygon.