How to prove that two parallel lines do not intersect?

How to prove that two parallel lines do not intersect? <br /><br />It is a postulate
(axiom) of Euclid's geometry. There are alternative geometries, where
this statement is not true. The metric geometries examine a space of
constant curvature. Zero curvature corresponds to the curvature of the
Euclidean geometry, positive - spherical, negative - Lobachevsky
geometry.