Question

given: lines p and q are parallel and r is a transversal.
prove: ∠2 ≅ ∠7

1. p || q, r is a transv.
2. a
3. b
4. ∠2 ≅ ∠7
5. given
6. vert. ∠s ≅
7. corr. ∠s thm.
8. transitive prop.

which statements could complete the proof?
a:
b:

Explanation:

Step1: Use vertical angles property

Since vertical angles are congruent, $\angle2\cong\angle4$.

Step2: Use corresponding angles theorem

Because $p\parallel q$ and $r$ is a transversal, by the corresponding angles theorem, $\angle4\cong\angle7$.

Step3: Use transitive property

By the transitive property of congruence, if $\angle2\cong\angle4$ and $\angle4\cong\angle7$, then $\angle2\cong\angle7$.

Answer:

A. $\angle2\cong\angle4$ (vertical angles), B. $\angle4\cong\angle7$ (corresponding angles theorem)