Question

given lines p and q are parallel and r is a transversal
prove ∠2 ≅ ∠7
which statements could complete the proof?
angle 3 is congruent to angle 6
angle 3 is congruent to angle 7
angle 6 is congruent to angle 7
angle 4 is congruent to angle 5

Explanation:

Step1: Vertical Angles

Vertical angles are congruent. So, $\angle2\cong\angle3$.

Step2: Corresponding Angles

Since $p\parallel q$ and $r$ is a transversal, by the corresponding angles theorem, $\angle3\cong\angle7$.

Step3: Transitive Property

By the transitive property of congruence (if $a = b$ and $b = c$, then $a = c$), since $\angle2\cong\angle3$ and $\angle3\cong\angle7$, we have $\angle2\cong\angle7$.

Answer:

A. $\angle2\cong\angle3$; B. $\angle3\cong\angle7$