Question

1. if two lines are cut by a transversal and corresponding angles are equal, which theorem proves the lines are parallel?

corresponding angles converse theorem
alternate interior angles theorem
consecutive interior angles theorem
corresponding angles theorem

Explanation:

• The Alternate Interior Angles Theorem states that if two parallel lines are cut by a transversal, then alternate interior angles are equal. It is not used to prove lines are parallel from angle equality.
• The Consecutive Interior Angles Theorem states that if two parallel lines are cut by a transversal, then consecutive interior angles are supplementary. It is not relevant here.
• The Corresponding Angles Theorem states that if two parallel lines are cut by a transversal, then corresponding angles are equal. It is the reverse of what we need.
• The Corresponding Angles Converse Theorem states that if two lines are cut by a transversal and corresponding angles are equal, then the lines are parallel. This is exactly what the question is asking for.

Answer:

Corresponding Angles Converse Theorem