<Li> SAS (Side - Angle - Side): If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent . </Li> <Li> SSS (Side - Side - Side): If three pairs of sides of two triangles are equal in length, then the triangles are congruent . </Li> <Li> ASA (Angle - Side - Angle): If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent . The ASA Postulate was contributed by Thales of Miletus (Greek). In most systems of axioms, the three criteria--SAS, SSS and ASA--are established as theorems . In the School Mathematics Study Group system SAS is taken as one (#15) of 22 postulates . </Li> <Li> AAS (Angle - Angle - Side): If two pairs of angles of two triangles are equal in measurement, and a pair of corresponding non-included sides are equal in length, then the triangles are congruent . AAS is equivalent to an ASA condition, by the fact that if any two angles are given, so is the third angle, since their sum should be 180 ° . ASA and AAS are sometimes combined into a single condition, AAcorrS--any two angles and a corresponding side . </Li>

If two triangles have three pairs of congruent angles