Which statement expresses the Converse of the Alternate Interior Angles Theorem?

Which statement expresses the Converse of the Alternate Interior Angles Theorem?

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

Answer: (B)

The main idea here is the converse relationship between angle equality and parallel lines. Alternate interior angles are the pair of angles located between the two lines and on opposite sides of the transversal. When the lines are parallel, those alternate interior angles are equal. The converse flips that: if those alternate interior angles are congruent, then the two lines must be parallel. Equality of those interior angles with respect to the same transversal means the lines never converge to meet, so they run parallel to each other. This is exactly why the statement “if a pair of alternate interior angles are congruent, then the lines are parallel” is the correct expression of the converse. The other options describe related, true ideas in different forms (the direct theorem, corresponding angles, or alternate exterior angles), but they are not the converse of the Alternate Interior Angles Theorem.

The main idea here is the converse relationship between angle equality and parallel lines. Alternate interior angles are the pair of angles located between the two lines and on opposite sides of the transversal. When the lines are parallel, those alternate interior angles are equal. The converse flips that: if those alternate interior angles are congruent, then the two lines must be parallel. Equality of those interior angles with respect to the same transversal means the lines never converge to meet, so they run parallel to each other. This is exactly why the statement “if a pair of alternate interior angles are congruent, then the lines are parallel” is the correct expression of the converse. The other options describe related, true ideas in different forms (the direct theorem, corresponding angles, or alternate exterior angles), but they are not the converse of the Alternate Interior Angles Theorem.