isosceles

Isosceles is a term used in geometry to describe figures with two sides of equal length. The most common use is for isosceles triangles, which have two congruent sides, called the legs, and a base opposite the vertex formed by the legs. In such a triangle, the angles opposite the equal sides are equal. The converse is also true: if two angles of a triangle are equal, the sides opposite those angles are equal.

In an isosceles triangle, the altitude drawn from the apex (the vertex between the two equal sides) to the base is also a median, an angle bisector, and a perpendicular to the base. This line acts as an axis of symmetry for the triangle, reflecting one leg onto the other.

The term is also used for other polygons that have two equal sides. The most common example beyond triangles is the isosceles trapezoid (or isosceles trapezium in some regions), a trapezoid with congruent legs. In an isosceles trapezoid, the base angles are equal, and the diagonals are equal in length. The figure exhibits symmetry about a line through the midpoints of the bases.

Originating from the Greek isos, equal, and skelos, leg, the word emphasizes balance or symmetry in length. While most discussions center on triangles and trapezoids, the general idea of isosceles applies to figures with two equal sides.