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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.

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# Homework Help: Proof That Isometries Preserve Parallel Lines

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