Congruent triangles are those that are identical, i.e. they have sides which are all the same lengtth and angles which are all the same size, compared with the corresponding sides and angles on the other triangle).
There are 5 conditions of congruency (what one may call theorems). If any one of these 5 conditions are met, the 2 shapes are congruent. The 4 conditions are:
1) SSS (all 3 pairs of CORRESPONDING sides are EQUAL)
2) SAS (2 pairs of CORRESPONDING sides and the CORRESPONDING included angle are EQUAL)
3) ASA (2 pairs of CORRESPONDING angles and the CORRESPONDING side between these 2 angles are EQUAL)
4) AAS (2 pairs of CORRESPONDING angles are EQUAL, and a
pair of CORRESPONDING non-included sides are EQUAL)
5) RHS (Both triangles contain a right angle, have a CORRESPONDING side that is EQUAL and have a CORRESPONDING hypotenuse - the side opposite the right angle - which are EQUAL)
