Question

use the diagram to the right. if ∠1 = ∠7, what theorem can you use to show that m||n? choose the correct answer below. a. the lines are parallel by the converse of the corresponding angles theorem. b. the lines are parallel by the converse of the alternate exterior angles theorem. c. the lines are parallel by the converse of the alternate interior angles theorem. d. the lines are parallel by the converse of the same - side interior angles theorem.

Explanation:

The Alternate Exterior Angles Theorem states that if two parallel lines are cut by a transversal, then the alternate - exterior angles are congruent. The converse of this theorem says that if alternate - exterior angles are congruent, then the lines are parallel. ∠1 and ∠7 are alternate exterior angles. Since ∠1 = ∠7, by the Converse of the Alternate Exterior Angles Theorem, the lines are parallel.

Answer:

B. The lines are parallel by the Converse of the Alternate Exterior Angles Theorem