Which statement is the ConVerse of the Alternate Exterior Angles Theorem?

Which statement is the ConVerse of the Alternate Exterior Angles Theorem?

• A. If the lines are parallel, alternate exterior angles are congruent.
• B. If a pair of alternate exterior angles are congruent, then the lines are parallel.
• C. If alternate interior angles are congruent, lines are parallel.
• D. If corresponding angles are congruent, lines are parallel.

Answer: (B)

The thing being tested is how a theorem about alternate exterior angles relates to its converse. The original statement says: when two lines are parallel, the alternate exterior angles formed with a transversal are congruent. The Converse flips the implication: if a pair of alternate exterior angles are congruent, then the lines are parallel. This is exactly the given correct choice. This is best because it directly mirrors the original theorem with the hypothesis and conclusion swapped, which defines a converse. The other statements involve different angle relationships: alternate interior angles (a different pairing) being congruent implies parallel lines, and corresponding angles being congruent also implies parallel lines—neither describes the Converse of the Alternate Exterior Angles Theorem.

The thing being tested is how a theorem about alternate exterior angles relates to its converse. The original statement says: when two lines are parallel, the alternate exterior angles formed with a transversal are congruent. The Converse flips the implication: if a pair of alternate exterior angles are congruent, then the lines are parallel. This is exactly the given correct choice.

This is best because it directly mirrors the original theorem with the hypothesis and conclusion swapped, which defines a converse. The other statements involve different angle relationships: alternate interior angles (a different pairing) being congruent implies parallel lines, and corresponding angles being congruent also implies parallel lines—neither describes the Converse of the Alternate Exterior Angles Theorem.