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.

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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.
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