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Parallel and Perpendicular Lines
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Conditions for Parallel Lines

Theorem. Converse of Same-Side Interior Angles Theorem
If two lines are cut by a transversal so that a pair of interior angles on the same side is supplementary, then the lines are parallel.

Given: ∠3 and ∠5 are same-side interior angles.
∠3 and ∠5 are supplementary.
Prove: m∥n

Proof: