<P> The two equal sides are called the legs and the third side is called the base of the triangle . The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs and base . Every isosceles triangle has an axis of symmetry along the perpendicular bisector of its base . The two angles opposite the legs are equal and 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> Euclid defined an isosceles triangle as a triangle with exactly two equal sides, but modern treatments prefer to define isosceles triangles as having at least two equal sides . The difference between these two definitions is that the modern version makes equilateral triangles (with three equal sides) a special case of isosceles triangles . A triangle that is not isosceles (having three unequal sides) is called scalene . "Isosceles" is a compound word, made from the Greek roots "isos" (equal) and "skelos" (leg). The same word is used, for instance, for isosceles trapezoids, trapezoids with two equal sides, and for isosceles sets, sets of points every three of which form an isosceles 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 . In the equilateral triangle case, since all sides are equal, any side can be called the base . </P> <P> Whether an isosceles triangle is acute, right or obtuse depends only on the angle at its apex . In Euclidean geometry, the base angles cannot be obtuse (greater than 90 °) or right (equal to 90 °) because their measures would sum to at least 180 °, the total of all angles in any Euclidean triangle . Since a triangle is obtuse or right if and only if one of its angles is obtuse or right, respectively, an isosceles triangle is obtuse, right or acute if and only if its apex angle is respectively obtuse, right or acute . In Edwin Abbott's book Flatland, this classification of shapes was used as a satire of social hierarchy: isosceles triangles represented the working class, with acute isosceles triangles lower in the hierarchy than right or obtuse isosceles triangles . </P>

What is the base of an isosceles triangle