Question

practice writing proofs and solving problems using converses of the parallel line theorems. which theorem correctly justifies why the lines m and n are parallel when cut by transversal k? converse of the corresponding angles theorem converse of the alternate interior angles theorem converse of the same side interior angles theorem converse of the alternate exterior angles theorem

Explanation:

The converse of the alternate exterior angles theorem states that if two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel. In the given diagram, the two \(50^{\circ}\) angles are alternate exterior angles. Since they are congruent, by the converse of the alternate exterior angles theorem, lines \(m\) and \(n\) are parallel.

Answer:

converse of the alternate exterior angles theorem