Today I reviewed several high school textbooks and all refer to SSS postulate as a criterion for congruence of two triangles. I was under impression that SSS is a theorem. Please help me understand what is going on.
From what I learned, SSS belongs to Euclid's Book 1 and is the eighth proposition. It is not a postulate and can be proven from the previous propositions, the four postulates and the axioms. The fifth postulate is only applicable from proposition 29 onwards, where the discrepancies came in.:)
It depends on what is considered as axiom. Indeed in Hilbert's axiom system (in a way a more elaborate and exact formulation of Euclid's axioms), we have SAS as axiom and the other triangle congruence statements as theorems.