Question

given: lines p and q are parallel and r is a transversal.
prove: ∠2 ≅ ∠7
which statements could complete the proof?
a:
b:

Explanation:

Step1: Use vertical angles theorem

Vertical angles are congruent. So, \(\angle2\cong\angle4\) (since they are vertical angles).

Step2: Use corresponding angles theorem

Since \(p\parallel q\) and \(r\) is a transversal, by the corresponding angles theorem, \(\angle4\cong\angle7\) (corresponding angles are congruent when two parallel lines are cut by a transversal).

Answer:

A: \(\angle2\cong\angle4\)
B: \(\angle4\cong\angle7\)