An isosceles triangle is a triangle with (at least) two equal sides. In the figure above, the two equal sides have length and the remaining side has length . This property is equivalent to two angles of the triangle
being equal. An isosceles triangle therefore has both two equal sides and two equal
angles. The name derives from the Greek iso (same) and skelos (leg).

A triangle with all sides equal is called an equilateral triangle, and a triangle with no sides equal is called a scalene
triangle. An equilateral triangle is
therefore a special case of an isosceles triangle having not just two, but all
three sides and angles equal. Another special case of an isosceles triangle is
the isosceles right triangle.

The height of the isosceles triangle illustrated above can be found from the Pythagorean
theorem as

or 2/3 the way from its vertex (Gearhart and Schulz 1990).

Considering the angle at the apex of the triangle and writing instead of , there is a surprisingly simple relationship between the area and vertex angle . As shown in the above diagram, simple
trigonometry gives

Erecting similar isosceles triangles on the edges of an initial triangle gives another triangle such that , , and concur. The triangles are therefore perspective
triangles.

No set of
points in the plane can determine only isosceles triangles.