Converse of Theorem 2

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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.

To prove:

AB||CD

Proof:

( Given)

(Vertically opposite angles)

(corresponding angles)

AB||CD ( corresponding angles

axiom)