Is triangle congruence SAS an axiom? I was wondering if there is a way to prove SAS in triangle congruence with Euclidean axioms.
Thank you for your help! 

The answer to this question is a bit complicated. It's not a straight yes or no.
Euclid claims to prove side-angle-side congruence in his Proposition 4, Book 1. He does this by "applying" one triangle to the other. Essentially, this means he moves one triangle until it coincides with the other. 
Euclid's proof is universally regarded as problematic from a logical standpoint, because there are absolutely no axioms in the Elements that tell you when, or in what ways, a figure can be "applied" to another.
There are modern axiom systems that are logically satisfactory, and they fill the gaps in Euclid in different ways. Some systems have axioms involving rigid motions, and in some cases it may be possible to give a proof similar to Euclid's.
The best-known modern axiom system intended to replace Euclid's, while staying close to his in spirit, is the one given by Hilbert in 1899 in Grundlagen der Geometrie.  Hilbert assumes as an axiom something slightly weaker than the full SAS property. Namely, Axiom IV-6 states that if two triangles have two corresponding sides and the angle between them equal, then they also have their remaining angles equal. From this, and his other axioms, Hilbert then proves that the remaining side must also be equal. 
So in Hilbert's case, two-thirds of the conclusion of the SAS property is assumed as an axiom, and the remaining one-third is proved.
