Question

1. state the theorem or postulate that proves a || b.
2. choose your answer here (your answer should be the most direct way to prove the lines parallel)

a. converse of the corresponding angles theorem
b. converse of the alternate interior angles theorem
c. converse of the same-side interior angles postulate
d. converse of the alternate exterior angles theorem

Explanation:

• Converse of the Alternate Exterior Angles Theorem: This theorem states that if two lines are cut by a transversal and the alternate exterior angles are congruent, then the two lines are parallel. In the given diagram, the angles shown are alternate exterior angles.
• Converse of the Corresponding Angles Theorem: Deals with angles in corresponding positions (not the case here).
• Converse of the Alternate Interior Angles Theorem: Deals with angles inside the two - line and on alternate sides (not the case here).
• Converse of the Same - Side Interior Angles Postulate: Deals with angles on the same side inside the two lines (not the case here).

Answer:

D. Converse of the Alternate Exterior Angles Theorem