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Parallel and Perpendicular Lines
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Parallel Lines and Transversals

Theorem. Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

In the figure below, if m∥n, then ∠3≅∠6 and ∠4≅∠5. You can prove this theorem for a particular angle pair and the other angle pairs can be proven similarly.

Given: m∥n cut by transversal t
Prove: ∠3≅∠6

Proof: