Question

∠3 ≅ ∠7
a) a || b; converse of corresponding angles theorem
b) ℓ || m; converse of corresponding angles theorem
c) a || b; alternate interior angles converse

Explanation:

1. First, identify the angles: $\angle 3$ and $\angle 7$ are corresponding angles (they are in the same relative position at each intersection where a transversal crosses the two lines $\ell$ and $m$ and the other lines $a$ and $b$).
2. The Converse of the Corresponding Angles Theorem states that if two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel.
3. Given $\angle 3 \cong \angle 7$, by the Converse of Corresponding Angles Theorem, the lines $\ell$ and $m$ (the lines cut by the transversal) must be parallel. So the correct answer is B as it concludes $\ell \parallel m$ using the Converse of Corresponding Angles Theorem.

Answer:

B) $\ell \parallel m$; Converse of Corresponding Angles Theorem