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

>>6
If it doesn't satisfy the triangle inequality (which was mistyped by >>3, but I'm guessing you get the idea), it isn't a metric.

At any rate, the Euclidean metric is brought into geometry through: rotational invariance (of distance), translational invariance (of distance), and the parallel postulate.