Proving Triangles are Congruent by AAS and HL

Students learn the third angle theorem, which states that if two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent. Students also learn the following theorems related to congruent triangles. If two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the triangles are congruent (Angle-Angle-Side or AAS). If the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent (Hypotenuse-Leg or HL). Students are then asked to determine whether given triangles are congruent, and name the postulate or theorem that is used.