Question

given the following picture, which lines, if any can be proved parallel if <8 = <10.

r || s
both sets of lines are parallel
none
m || n

Explanation:

Step1: Recall the converse of the alternate interior angles theorem

If two lines are cut by a transversal and the alternate interior angles are congruent, then the two lines are parallel.

Step2: Analyze the relationship between \(\angle8\) and \(\angle10\)

\(\angle8\) and \(\angle10\) are alternate interior angles formed by lines \(r\) and \(s\) and a transversal.
Since \(\angle8=\angle10\), by the converse of the alternate interior angles theorem, \(r\parallel s\)

Answer:

\(r\parallel s\)