(A) : The set of points in one side equidistant from a given line forms a line
Postulate V : If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough
Prove that postulate V implies (A)
Proof : From postulate I through V, we have Euclid's proposition I.34 i.e. in a parallelogram, the opposites and angles are congruent.
How can we finish the proof ?
Add : This is theorem 3.4 in the book geometry from a differential viewpoint - McCleary