# Converse of Alternate Interior Angles Theorem Proof

Converse alternate interior angles theorem states that if two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.

## Converse of Alternate Interior Angles Theorem Proof

STATEMENT:
If a transversal intersects two lines in such a way that a pair of alternate interior angles are equal, then the two lines are parallel.

Given:
Transversal EFGH intersects lines AB and CD such that a pair of alternate E are equal.

Image  To prove:
AB||CD

PROOF:  (Vertically opposite angles) (corresponding angles)
AB||CD ( corresponding angles axiom)

Since the corresponding angles of the lines AB and CD are equal, the lines are parallel.
Thus the converse of alternate interior angles theorem is proved.

Converse alternate interior angles theorem states that if two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.

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