Pythagoras' theorem

Pythagoras' theorem is a natural consequence of having the typical metric on a plane. However, in his proof, he never mentions what metric he uses - somehow, he must have snuck the metric in. Where does his proof assume the usual metric?

http://en.wikipedia.org/wiki/Pythagorus's_theorem#Proof_using_similar_triangles

"The shortest path between any two points is a straight line"

I'm pretty sure that's one of the axioms of classical geometry. Too lazy to look.