What does the Converse of the Corresponding Angles Postulate state?

What does the Converse of the Corresponding Angles Postulate state?

• A. If two lines are parallel, corresponding angles are congruent.
• B. If corresponding angles are congruent, then the lines are parallel.
• C. If alternate interior angles are congruent, lines are parallel.
• D. If two lines are perpendicular, corresponding angles are congruent.

Answer: (B)

The statement tested is the Converse of the Corresponding Angles Postulate: if two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel. This is the logical reverse of the usual postulate, which says that if two lines are parallel, then corresponding angles are congruent. Here, the equal corresponding angles guarantee that the lines never meet, so they must be parallel. This is a practical way to prove parallelism from angle measurements when a transversal runs across the lines. The other ideas either describe the direct postulate (parallel implies congruent corresponding angles), refer to a different criterion (alternate interior angles), or involve a condition (perpendicularity) that doesn’t characterize parallel lines by corresponding angles.

The statement tested is the Converse of the Corresponding Angles Postulate: if two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel. This is the logical reverse of the usual postulate, which says that if two lines are parallel, then corresponding angles are congruent. Here, the equal corresponding angles guarantee that the lines never meet, so they must be parallel. This is a practical way to prove parallelism from angle measurements when a transversal runs across the lines. The other ideas either describe the direct postulate (parallel implies congruent corresponding angles), refer to a different criterion (alternate interior angles), or involve a condition (perpendicularity) that doesn’t characterize parallel lines by corresponding angles.