Question

use the diagram to the right. if ∠3≅∠9, what theorem can you use to show that j||k? choose the correct answer below. a. the lines are parallel by the converse of the alternate interior angles theorem. b. the lines are parallel by the converse of the corresponding angles theorem. c. the lines are parallel by the converse of the same - side interior angles theorem. d. the lines are parallel by the converse of the alternate exterior angles theorem.

Explanation:

Step1: Identify angle - type relationship

$\angle3$ and $\angle9$ are alternate exterior angles.

Step2: Recall parallel - line theorem

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. Since $\angle3\cong\angle9$, we can use this theorem to show $j\parallel k$.

Answer:

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