Question

which lines must be parallel?
a r and s
b p and q
c p and r
d q and s
e cannot be determined
given: ∠2 ≅ ∠4

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 given angles

Given \( \angle2\cong\angle4\). These are alternate interior angles for lines \(p\) and \(q\) with the transversal (the line that intersects both \(p\) and \(q\)).
By the converse of the alternate interior angles theorem, if \( \angle2\cong\angle4\), then \(p\parallel q\).

Answer:

B. \(p\) and \(q\)