Isosceles triangle

Isosceles triangle
Isosceles triangle
Type	triangle
Edges and vertices	3
Schläfli symbol	( ) ∨ { }
Symmetry group	Dih2, [ ], (*), order 2
Properties	convex, cyclic
Dual polygon	Self-dual

In geometry, an isosceles triangle (/aɪˈsɒsəliːz/) is a triangle that has two sides of equal length and two angles of equal measure. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case. Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids.

The mathematical study of isosceles triangles dates back to ancient Egyptian mathematics and Babylonian mathematics. Isosceles triangles have been used as decoration from even earlier times, and appear frequently in architecture and design, for instance in the pediments and gables of buildings.

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 reflection symmetry across the perpendicular bisector of its base, which passes through the opposite vertex and divides the triangle into a pair of congruent right triangles. The two equal angles at the base (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.