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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.

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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.:)

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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.

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  • $\begingroup$ So, even in the Hilbert's system, SSS is a theorem. $\endgroup$ – Dusan Nesic Oct 20 '13 at 17:51

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