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

>>9
http://en.wikipedia.org/wiki/Inner_product
http://en.wikipedia.org/wiki/Metric_space

Minkowski spaces are not inner product spaces, and the "weak inner product" does not give a metric. Calling them such doesn't change the fact that they do not satisfy the appropriate axioms.