Question

given: ∠1 ≅ ∠8
which lines must be parallel?
a r and s
b p and q
c p and r
d q and s
e p and s

Explanation:

Step1: Use vertical angles property

Since \( \angle1\cong\angle2 \) (vertical angles), and given \( \angle1\cong\angle8 \), then \( \angle2\cong\angle8 \) (transitive property).

Step2: Apply parallel line theorem

If two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel. Here, lines \( p \) and \( s \) are cut by transversal \( r \), and \( \angle2\) and \( \angle8 \) are corresponding angles.

Answer:

E. \( p \) and \( s \)