I have a question about Hilbert's axiomatic system. In this system we have the SAS (Side-Angle-Side) congruence criterion as an axiom, and then we prove the SSS (Side-Side-Side) and ASA (Angle-Side-Angle) criteria as theorems. I was wondering then if it was possible to have SSS as an axiom (eventually adding something more) and prove SAS as a theorem, and then again with ASA instead. I have tried to do some research but I didn't find anything at all. Any reference or result would be welcome, thanks a lot in advance.
2026-02-23 13:47:46.1771854466
Using another congruence criterion as axiom in Hilbert's axiomatic geometry
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