Converse of the Same-Side Interior Angles Theorem states that if two coplanar lines are cut by a transversal so that a pair of same-side interior angles are supplementary, then the lines are

Converse of the Same-Side Interior Angles Theorem states that if two coplanar lines are cut by a transversal so that a pair of same-side interior angles are supplementary, then the lines are

• A. Parallel
• B. Perpendicular
• C. Skew
• D. Intersecting

Answer: (A)

The key idea is that if a pair of same-side interior angles formed by a transversal add up to 180 degrees, the two lines being cut must be parallel. Same-side interior angles are the interior angles on the same side of the transversal; when the lines are parallel, those two interior angles are supplementary, sum to a straight angle. So observing a supplementary pair of same-side interior angles confirms the lines run parallel. Perpendicular would require a right-angle relationship, which isn’t implied by a 180-degree sum of those interior angles. Skew isn’t possible for coplanar lines with a transversal, and intersecting lines wouldn’t produce the definite parallel condition given by the supplementary interior angles. Therefore, parallel is the correct conclusion.

The key idea is that if a pair of same-side interior angles formed by a transversal add up to 180 degrees, the two lines being cut must be parallel. Same-side interior angles are the interior angles on the same side of the transversal; when the lines are parallel, those two interior angles are supplementary, sum to a straight angle. So observing a supplementary pair of same-side interior angles confirms the lines run parallel.

Perpendicular would require a right-angle relationship, which isn’t implied by a 180-degree sum of those interior angles. Skew isn’t possible for coplanar lines with a transversal, and intersecting lines wouldn’t produce the definite parallel condition given by the supplementary interior angles. Therefore, parallel is the correct conclusion.