Question

given: lines p and q are parallel and r is a transversal. prove: ∠2≅∠7 statements reasons 1. p || q, r is a transv. 1. given 2. a 2. vert. ∠s ≅ 3. b 3. corr. ∠s thm. 4. ∠2≅∠7 4. transitive prop. which statements could complete the proof? a: b: 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: Identify vertical - angle congruence

$\angle2\cong\angle3$ (vertical angles are congruent)

Step2: Identify corresponding - angle congruence

Since $p\parallel q$ and $r$ is a transversal, $\angle3\cong\angle7$ (corresponding - angles theorem)

Step3: Apply transitive property

If $\angle2\cong\angle3$ and $\angle3\cong\angle7$, then $\angle2\cong\angle7$ (transitive property)

Answer:

A: $\angle2\cong\angle3$
B: $\angle3\cong\angle7$