Reports a proof of a classical geometry problem. The proposition is - In any triangle there are two equal sides, if the angles opposite these sides have angle bisectors with equal lengths. (RP)

A problem involving the search for an equivalence class of triangles is viewed to provide several exciting and satisfying moments of insight. After solving the original problem, there is a brief discussion of a slight variation and several notes regarding related theorems and ideas. References for additional exploration are provided. (MP)