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Converse of the Parallel Lines Theorem

The Corresponding Angles Theorem states that if parallel lines are cut by a transversal, then their corresponding angles are congruent. Use this GeoGebra construction to determine if the converse of that theorem is true. If two lines are cut by a transversal so that the corresponding angles are congruent, are the lines always parallel? Is there any way to construct the line through the transversal with congruent corresponding angles so that they are not parallel?