<P> By the isosceles triangle theorem, the two angles opposite the legs are themselves equal, while if the third side is different then the third angle is different . By the Steiner--Lehmus theorem, every triangle with two angle bisectors of equal length is isosceles . </P> <P> Every isosceles triangle has an axis of symmetry along the perpendicular bisector of its base . In a non-equilateral isosceles triangle this axis is also the Euler line of the triangle, and one of the two axes of the Steiner inellipse . The two angles opposite the legs are always acute, so the classification of the triangle as acute, right, or obtuse depends only on the angle between its two legs . </P> <P> "Isosceles" is a compound word, made from "isos" (equal) and skelos (leg). The same word is used, for instance, for isosceles trapezoids, trapezoids with two equal sides, and for sets of more than three points that have only two distinct distances between pairs of points . A triangle that is not isosceles (having three unequal sides) is called a scalene triangle . </P> <P> In an isosceles triangle that has exactly two equal sides, the equal sides are called legs and the third side is called the base . The angle included by the legs is called the vertex angle and the angles that have the base as one of their sides are called the base angles . The vertex opposite the base is called the apex . </P>

If the two equal sides of an isosceles triangle have length a