quality:correction, quality:corruption, structural:expansion
Isosceles subdivision of other shapes

For any integer n ≥ 4 {\displaystyle n\geq 4}, any triangle can be partitioned into n {\displaystyle n} 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. Similarly, an acute triangle can be partitioned into three isosceles triangles by segments from its circumcenter, but this method does not work for obtuse triangles, because the circumcenter lies outside the triangle.

Generalizing the partition of an acute triangle, any cyclic polygon that contains the center of its circumscribed circle can be partitioned into isosceles triangles by the radii of this circle through its vertices. The fact that all radii of a circle have equal length implies that all of these triangles are isosceles. This partition can be used to derive a formula for the area of the polygon as a function of its side lengths, even for cyclic polygons that do not contain their circumcenters. This formula generalizes Heron's formula for triangles and Brahmagupta's formula for cyclic quadrilaterals.

Either diagonal of a rhombus divides it into two congruent isosceles triangles. Similarly, one of the two diagonals ofa kite divides it into two isosceles triangles, which are not congruent except when the kite is a rhombus.