Question

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:

• Converse of the corresponding angles theorem: States that if two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel. But in the given figure, the angles are not in the corresponding angles position.
• Converse of the alternate interior angles theorem: States that if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel. The given angles are not alternate interior angles.
• Converse of the same - side interior angles theorem: States that if two lines are cut by a transversal and the same - side interior angles are supplementary, then the lines are parallel. The given angles are not same - side interior angles.
• 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 figure, the two \(50^{\circ}\) angles are alternate exterior angles. Since they are congruent (\(50^{\circ}=50^{\circ}\)), by the converse of the alternate exterior angles theorem, lines \(m\) and \(n\) are parallel.

Answer:

converse of the alternate exterior angles theorem