Hey guys, just wanted to get a quick check that this proof is sound. 1. The problem statement, all variables and given/known data Let L, K be two parallel lines, and let F be an isometry. Prove that F(L) & F(K) are parallel. 2. Relevant Equations If P and Q are points on the plane and F is an isometry, the distance PQ = the distance F(PQ). 3. The attempt at a solution 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.