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Converse Alternate Interior Angles Theorem

Rule

Converse Alternate Interior Angles Theorem

If a pair of alternate interior angles formed by a transversal are congruent, the lines crossed are parallel lines.
For example, in the figure below the lines A  BA\ ||\ B because the alternate interior angles have the same measure.

The theorem is named the Converse Alternate Interior Angles Theorem because the same thing holds true but in opposite order.