Let L, K be two parallel lines, and let F be an isometry. Prove that F(L) & F(K) are parallel.

This is what I have for a proof. I'm looking for someone to tell me if it's sound:

Let P be a point on L and Q a point on K. By definition of parallel lines, L & K have no point in common. Because F is an isometry, the distance PQ = the distance F(PQ). Therefore, F(L) & F(K) must also have no point in common. Thus F(L) & F(K) are parallel.

Question

Let L, K be two parallel lines, and let F be an isometry. Prove that F(L) & F(K) are parallel.

This is what I have for a proof. I'm looking for someone to tell me if it's sound:

Let P be a point on L and Q a point on K. By definition of parallel lines, L & K have no point in common. Because F is an isometry, the distance PQ = the distance F(PQ). Therefore, F(L) & F(K) must also have no point in common. Thus F(L) & F(K) are parallel.

zarkon · Answer

sounds fine...though I"ve had a lot of wine so you might want a second opinion.

anonymous · Answer

Ha! Thanks a lot enjoy the rest of your Thanksgiving :P

zarkon · Answer

will do...you too