If two lines are cut by a transversal and the corresponding angles are congruent, what does that imply?

If two lines are cut by a transversal and the corresponding angles are congruent, what does that imply?

• A. The lines are parallel.
• B. The lines are perpendicular.
• C. The lines are skew.
• D. Nothing can be concluded.

Answer: (A)

Corresponding angles are the pair of angles that occupy the same position at each intersection formed by the transversal with the two lines. If those corresponding angles have equal measure, the two lines must run in the same direction and never meet, so they are parallel. This is a standard rule: congruent corresponding angles imply parallel lines, and parallel lines yield congruent corresponding angles. Perpendicular would require a 90-degree angle, which isn't required by the congruence of corresponding angles. Skew lines aren’t in the same plane and aren’t cut by a single transversal in the usual sense, so that scenario doesn’t apply here. Therefore, the correct conclusion is that the lines are parallel.

Corresponding angles are the pair of angles that occupy the same position at each intersection formed by the transversal with the two lines. If those corresponding angles have equal measure, the two lines must run in the same direction and never meet, so they are parallel. This is a standard rule: congruent corresponding angles imply parallel lines, and parallel lines yield congruent corresponding angles. Perpendicular would require a 90-degree angle, which isn't required by the congruence of corresponding angles. Skew lines aren’t in the same plane and aren’t cut by a single transversal in the usual sense, so that scenario doesn’t apply here. Therefore, the correct conclusion is that the lines are parallel.