Proving congruent with Euclidean axioms

[ali PMPAINT]

TL;DR

Proving SAS, SSS, ASA and that in a triangle, the bigger the opposite angle, the bigger the side is and in an Isosceles triangle, the two angles are ‌equal.

So, given one, you can prove the others, but I don't know how to prove one with using the five axioms.

 

[stevendaryl]

According to http://www.math.uga.edu/sites/default/files/inline-files/10.pdf, these rules are not proved using Euclid's axioms, but are proved using unstated rules about moving triangles around.

 

[ali PMPAINT]

According to http://www.math.uga.edu/sites/default/files/inline-files/10.pdf, these rules are not proved using Euclid's axioms, but are proved using unstated rules about moving triangles around.

Thank you, could you introduce me another one but this time for real numbers' axioms and basic proofs?