Problem #WSP-000163

Problem

Let $ABC$ and $A_1{B}_1{C}_1$ be two triangles with the following properties: $AB=A_1{B}_1$, $AC=A_1{C}_1$, and angles $\mathrm{\angle }BAC=\mathrm{\angle }{B}_1{A}_1{C}_1$. Then the triangles $ABC$ and $A_1{B}_1{C}_1$ are congruent. This is usually known as the “side-angle-side" criterion for congruence.