How many congruence criteria are there for triangles and what does each mean?

Five congruence criteria: SSS (3 sides equal), SAS (2 sides and included angle), ASA (2 angles and included side), AAS (2 angles and any side), RHS (right angle, hypotenuse, one side). SSA is NOT valid because knowing 2 sides and a NON-included angle can produce two different triangles or none. Example: if you have angle A, side AB, and side BC (not adjacent to angle A), you might be able to draw two different triangles with those measurements. This ambiguity makes it unreliable as a congruence test. Similarly, AAA is not a congruence test (it gives similarity, not congruence — triangles can be the same shape but different sizes).