Question

given: ∠1 ≅ ∠3
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

Explanation:

Step1: Recall the converse of the corresponding angles postulate

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

Step2: Identify the lines and transversal

Here, \(\angle1\) and \(\angle3\) are corresponding angles. The transversal is line \(r\) (assuming the lines \(p\) and \(q\) are cut by a transversal). Since \(\angle1\cong\angle3\), by the converse of the corresponding angles postulate, lines \(p\) and \(q\) must be parallel.

Answer:

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