angle-side-angle theorem

The angle-side-angle (ASA) theorem is a fundamental concept in Euclidean geometry. It states that if two angles and the side between them in one triangle are equal to the corresponding two angles and the included side in another triangle, then the two triangles are congruent, meaning they have the same shape and size.1

This theorem is one of three ways to prove triangle congruence, alongside the side-side-side (SSS) and side-angle-side (SAS) theorems. The ASA theorem was known to ancient Greek mathematicians, with Thales of Miletus credited with proving several geometric theorems, including one stating that two triangles are congruent if two angles and a side are equal. This theorem is crucial for establishing geometric relationships and can be applied in various contexts, such as calculating unknown measurements using similar triangles.12