Steiner-Lehmus Theorem

The Steiner-Lehmus Theorem states that a triangle with two internal angle bisectors of equal length, each measured from a vertex to the opposite side, must be isosceles. Named for Jakob Steiner and Daniel Christian Ludolph Lehmus, it is a classical result of elementary triangle geometry notable for being considerably harder to prove directly than its converse, that an isosceles triangle has two equal angle bisectors, which follows immediately from symmetry.