 If the two equal sides have length formula_2 and the other side has length formula_3, then the internal angle bisector formula_22 from one of the two equal-angled vertices satisfies
as well as
and conversely, if the latter condition holds, an isosceles triangle parametrized by formula_2 and formula_22 exists.The Steiner–Lehmus theorem states that every triangle with two angle bisectors of equal lengths is isosceles.It was formulated in 1840 by C. L. Lehmus.