Steiner-Lehmus theorem

The Steiner-Lehmus theorem is that any triangle that has two equal angle bisectors (each measured from a vertex to the opposite sides) is an isosceles triangle. In 1840, a Berlin professor Ludolph Lehmus wondered if this statement is true, given that it is the inverse of the already proven rule: If a triangle isosceles then two of its internal bisectors are equal. He put the problem to Jakob Steiner who was quickly able to show its validity. Shortly after, Lehmus himself found a neater proof and it is has since become a favorite pastime of geometry hobbyists to search for still simpler proofs of the theorem.