Slightly off topic but you can take the "Pythagorean theorem" as an axiom - given the first 4 Euclidean axioms it turns out that the 5th axiom is exactly equiva

Slightly off topic but you can take the "Pythagorean theorem" as an axiom - given the first 4 Euclidean axioms it turns out that the 5th axiom is exactly equivalent to the Pythagorean theorem. You can equivalently start with the parallel postulate and derive Pythogoras or start with Pythagoras and derive the parallel postulate.