# Steiner-Lehmus Theorem

## Theorem

Let $ABC$ be a triangle.

Denote the lengths of the angle bisectors through the vertices $A$ and $B$ by $\omega_\alpha$ and $\omega_\beta$.

Let $\omega_\alpha = \omega_\beta$.

Then $ABC$ is an isosceles triangle.

## Source of Name

This entry was named for Jakob Steiner and Daniel Christian Ludolph Lehmus.