Question

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

1. p || q, r is a transv.\
2. a\
3. b\
4. ∠2 ≅ ∠7\

\
reasons\

1. given\
2. vert. ∠’s ≅\
3. corr. ∠’s thm.\
4. transitive prop.\

\
which statements could complete the proof?\
a: \
\
b:

Explanation:

Step1: Identify vertical angles

$\angle 2 \cong \angle 4$ (Vertical angles are congruent)

Step2: Identify corresponding angles

$\angle 4 \cong \angle 7$ (Corresponding angles of parallel lines cut by a transversal are congruent)

Step3: Apply transitive property

If $\angle 2 \cong \angle 4$ and $\angle 4 \cong \angle 7$, then $\angle 2 \cong \angle 7$

Answer:

A: $\boldsymbol{\angle 2 \cong \angle 4}$
B: $\boldsymbol{\angle 4 \cong \angle 7}$