Prove that the following statements are logically equivalent:
(1) Hilbert's Euclidean Parallel Postulate
(2) If k is parallel to l, m is perpendicular to k, and n is perpendicular to l, then either m = n or m is parallel to n.
Prove that the following statements are logically equivalent:
(1) Hilbert's Euclidean Parallel Postulate
(2) If k is parallel to l, m is perpendicular to k, and n is perpendicular to l, then either m = n or m is parallel to n.