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Parallel and Perpendicular Lines
A
B
C
D
E
. . . .

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: mn

Proof: