Question

1. (l27) given: ∠2 and ∠7 are supplementary prove: m || n a. definition of parallel lines b. if two lines form congruent alternate interior angles with a transversal, then the lines are parallel. c. if two lines form congruent corresponding angles, then the lines are parallel. d. if two lines form supplementary interior angles on the same side of a transversal, then the lines are parallel. e. if two lines form congruent alternate exterior angles, then the lines are parallel.

Explanation:

Step1: Recall angle - line relationship

If two lines are cut by a transversal, and a pair of same - side interior angles are supplementary, the lines are parallel. ∠2 and ∠7 are same - side interior angles. Given that they are supplementary, we can use the converse of the same - side interior angles postulate.

Step2: Apply the postulate

Since ∠2 and ∠7 are supplementary (given), by the converse of the same - side interior angles postulate, if two lines form supplementary same - side interior angles with a transversal, then the lines are parallel. So, m || n.

Answer:

We use the fact that if two lines form supplementary same - side interior angles with a transversal, then the lines are parallel (Option C). The key here is that ∠2 and ∠7 are same - side interior angles and their supplementary nature implies m || n.