Proving Lines Parallel

After a quick glance at my room, I noticed the overwhelming amount of parallel lines that could be found in my blinds. But, were these lines surely parallel?

We can prove lines parallel in various ways. According the Theorem 3-6, if two lines are cut by a transversal and same side interior angles are supplementary, then the lines are parallel.

We can see in the above photo that this theorem has been proven. After adding in a transversal line, we can see that the same side interior angles, ∠1 and ∠2, are supplementary, therefore proving the lines must be parallel. (~RO5 )