Two parallel lines are cut by a transversal. Which statement about a pair of corresponding angles is true?

Two parallel lines are cut by a transversal. Which statement about a pair of corresponding angles is true?

• A. They are congruent
• B. They are vertical
• C. They are complementary
• D. They are supplementary

Answer: (D)

When a transversal crosses two parallel lines, corresponding angles have equal measures. These angles occupy the same relative position at each intersection, and the parallelism guarantees that the "shape" of the crossing is preserved from one intersection to the other. So if one corresponding angle measures, say, 60 degrees, the other corresponding angle must also be 60 degrees. That makes them congruent. This is different from vertical angles, which are opposite one another at a single intersection, and it’s different from being complementary or supplementary, which depend on specific sums (not a general property of corresponding angles). A related true fact is that interior angles on the same side of the transversal are supplementary, but that describes a different pairing of angles.

When a transversal crosses two parallel lines, corresponding angles have equal measures. These angles occupy the same relative position at each intersection, and the parallelism guarantees that the "shape" of the crossing is preserved from one intersection to the other. So if one corresponding angle measures, say, 60 degrees, the other corresponding angle must also be 60 degrees. That makes them congruent.

This is different from vertical angles, which are opposite one another at a single intersection, and it’s different from being complementary or supplementary, which depend on specific sums (not a general property of corresponding angles). A related true fact is that interior angles on the same side of the transversal are supplementary, but that describes a different pairing of angles.