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. n||x by the same - side interior angles theorem b. m||y by the corresponding angles theorem c. n||m by the alternate exterior angles theorem d. x||y 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 relationships

When two parallel lines are cut by a transversal, different angle - angle relationships can prove parallelism. Corresponding angles are equal when lines are parallel. Alternate interior angles are equal when lines are parallel. Alternate exterior angles are equal when lines are parallel. Same - side interior angles are supplementary when lines are parallel.

Step2: Analyze the given angle $\angle3\cong\angle5$

$\angle3$ and $\angle5$ are alternate exterior angles. According to the Alternate Exterior Angles Theorem, if alternate exterior angles are congruent, then the lines are parallel. In the context of the lines in the problem, if $\angle3\cong\angle5$, then $n\parallel m$.

Answer:

C. $n\parallel m$ by the Alternate Exterior Angles Theorem