Editing Isosceles triangle (section)

==Isosceles subdivision of other shapes==
[[File:Cyclic pentagon isosceles partition.svg|thumb|Partition of a [[cyclic polygon|cyclic pentagon]] into isosceles triangles by radii of its circumcircle]]
For any integer <math>n \ge 4</math>, any [[triangle]] can be partitioned into <math>n</math> isosceles triangles.<ref>{{harvtxt|Lord|1982}}. See also {{harvtxt|Hadamard|2008|loc=Exercise 340, p. 270}}.</ref>
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.{{sfnp|Posamentier|Lehmann|2012|page=24}}
Similarly, an [[acute triangle]] can be partitioned into three isosceles triangles by segments from its circumcenter,{{sfnp|Bezdek|Bisztriczky|2015}} but this method does not work for obtuse triangles, because the circumcenter lies outside the triangle.{{sfnp|Harris|Stöcker|1998|page=75}}

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 quadrilateral]]s.{{sfnp|Robbins|1995}}

Either [[diagonal]] of a [[rhombus]] divides it into two [[Congruence (geometry)|congruent]] isosceles triangles. Similarly, one of the two diagonals of
a [[Kite (geometry)|kite]] divides it into two isosceles triangles, which are not congruent except when the kite is a rhombus.{{sfnp|Usiskin|Griffin|2008|page=51}}