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

>>1
Euclidean geometry (assumption) = usual metric.

>>2
I'm not sure if it's an axiom, but it is only true for Euclidean geometry.

>>3
phail for metrics that describe pseudoriemannian manifolds (ie GR)

>>4
Probably.