 A much older theorem, preserved in the works of Hero of Alexandria,
states that, for an isosceles triangle with base formula_3 and height formula_1, the side length of the inscribed square on the base of the triangle is

For any integer formula_35, any triangle can be partitioned into formula_36 isosceles triangles.In a right triangle, the median from the hypotenuse (that is, the line segment from the midpoint of the hypotenuse to the right-angled vertex) divides the right triangle into two isosceles triangles.This is because the midpoint of the hypotenuse is the center of the circumcircle of the right triangle, and each of the two triangles created by the partition has two equal radii as two of its sides.