Question

a. in the figure above ∠1 ≅ ∠4. is u || v? choose your answer... how do you know? choose your answer...

Explanation:

Step1: Check the relationship between angles

If \(u\parallel v\), then \(\angle1\cong\angle4\) (alternate exterior angles). But if \(u\) is not parallel to \(v\), \(\angle1\) and \(\angle4\) are not congruent.

Step2: Determine the condition

Since \(\angle1\cong\angle4\) is given, by the converse of the alternate exterior angles theorem, if two lines are cut by a transversal and alternate exterior angles are congruent, then the two lines are parallel.

Answer:

Yes, \(u\parallel v\) because \(\angle1\cong\angle4\) (by the converse of the alternate - exterior angles theorem).