Definition of congruence of triangles.

Question

In school level geometry,we studied congruence of triangles.Where it is defined that two triangles are congruent if they have same shape and size.But this is not a precise definition,what does it mean mathematically.I know some criteria for congruence which are $SSS,SAS,ASA,AAS,RHS$ criteria.But which one should I take as definition.Which one is the standard definition?

Answer 1

One fairly typical text, Geometry by Moise & Downs, takes SAS as a postulate and proves all the others.

It might be interesting to note that two triangles can have 5 of the six parts congruent and yet not be congruent themselves.