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Congruent
There's lots of useful things you can discover when parallel lines are cut by a transversal, most of them having to do with angle relationships. Corresponding angles are congruent, alternate interior angles are congruent, same side or consecutive interior angles are supplementary, alternate exterior angles are congruent, and vertical angles are congruent.
Show that corresponding angles are congruent?
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Sure. Just as long as the transversal is perpendicular to the parallel lines.
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If two parallel lines are intersected by a transversal, then the corresponding angles are congruent. This is the transversal postulate. So the answer is the lines would be parallel. This means that the statement is true.
The lines are parallel. The only time you will see correpsonding, alternate interior, and alternate exterior angles is with a parallel transversal line.
Parallel lines cut by a transversal form congruent alternate interior angles.
a transversal line If a transversal intersects two parallel lines, then the alternate interior angles are congruent.