To prove lines are parallel, you need a third line. We at Shmoop (and the rest of the world) call it a transversal.

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Parallel Lines and Transversals 
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Slopes of Parallel and Perpendicular Lines 
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Proving Lines are Perpendicular 
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Proving Lines are Parallel 
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Lines, Segments and Rays 
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Shmoop? What is that? 
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Jane Eyre Summary 
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What is Shmoop?