Question

use the given information to determine which lines, if any, are parallel. justify each conclusion with a theorem. determine the pair of parallel lines and justify the conclusion. select all that apply. a. r║s by the alternate exterior angles theorem b. m║n by the corresponding angles theorem c. r║m by the same - side interior angles theorem d. s║n by the alternate interior angles theorem e. there is not enough information to prove whether or not any of the lines are parallel.

Explanation:

Step1: Recall angle - parallel line theorems

If two lines are cut by a transversal, corresponding angles being equal implies the lines are parallel. Alternate - interior angles being equal implies the lines are parallel. Alternate - exterior angles being equal implies the lines are parallel. Same - side interior angles being supplementary implies the lines are parallel.

Step2: Analyze given information

We are given that \(\angle7\cong\angle9\). \(\angle7\) and \(\angle9\) are alternate - exterior angles.

Step3: Apply the theorem

By the Alternate Exterior Angles Theorem, if two lines are cut by a transversal and the alternate - exterior angles are congruent, then the two lines are parallel. Here, the lines \(r\) and \(s\) are cut by a transversal, and since \(\angle7\cong\angle9\), we can conclude that \(r\parallel s\).

Answer:

A. \(r\parallel s\) by the Alternate Exterior Angles Theorem