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 corresponding angles theorem states that if two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel.
• In the given diagram, the two \(50^{\circ}\) angles are corresponding angles.
• The converse of the alternate interior angles theorem would apply if the angles were between the two lines and on opposite sides of the transversal.
• The converse of the same - side interior angles theorem would apply if the sum of the angles was \(180^{\circ}\).
• The converse of the alternate exterior angles theorem would apply if the angles were outside the two lines and on opposite sides of the transversal.

Answer:

converse of the corresponding angles theorem