🧵 ASA Congruence rule

Anonymous at Sat, 8 Jun 2024 14:07:45 UTC No. 16221907

Using Hilbert's axiomatic system, can someone give me an elementary proof of the angle-side-angle congruence rule. Every proof I have come across relies on contradiction and justification from the diagram (pic related - <BCP can't be equal to <BCA since P is between B and A). I know that it seems obvious but there has to be a rigorous proof, based for example on the crossbar theorem.

As for the other congruence rules, SAS is taken as an axiom and there is a decent proof of SSS on cut-the-knot. This is literally all that is missing.