The Angle-Angle-Side (AAS) theorem is a principle in geometry that helps determine the congruence of triangles. According to this theorem, if two angles and a non-included side of one triangle are respectively equal to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent. This means they have the same shape and size. AAS is useful in various applications, such as in trigonometry and construction, where determining the properties of triangles is essential. By establishing congruence through AAS, one can solve problems involving triangle similarity and geometric proofs effectively.