Question

use the given information to determine which lines, if any, are parallel. justify each conclusion with a theorem. ∠1 = ∠8. determine the pair of parallel lines and justify the conclusion. select all that apply. a. s||v by the alternate interior angles theorem b. r||s by the alternate exterior angles theorem c. r||u by the same - side interior angles theorem d. s||v by the corresponding angles theorem e. there is not enough information to prove whether or not any of the lines are parallel. video textbook get more help - clear all check answer review progress question 5 of 16 back next

Explanation:

Step1: Recall angle - related parallel - line theorems

The Alternate Interior Angles Theorem states that if alternate interior angles are congruent, then the lines are parallel. The Alternate Exterior Angles Theorem states that if alternate exterior angles are congruent, then the lines are parallel. The Same - Side Interior Angles Theorem states that if same - side interior angles are supplementary, then the lines are parallel. The Corresponding Angles Theorem states that if corresponding angles are congruent, then the lines are parallel.

Step2: Analyze given angle condition

We are given that $\angle1\cong\angle8$. $\angle1$ and $\angle8$ are alternate exterior angles.

Step3: Determine parallel lines

By the Alternate Exterior Angles Theorem, if $\angle1\cong\angle8$, then the lines $r$ and $s$ are parallel.

Answer:

B. $r\parallel s$ by the Alternate Exterior Angles Theorem