1. **State the problem:** Given two parallel lines $a \parallel b$ cut by a transversal, prove that $\angle 3 \cong \angle 6$. 2. **Recall the relevant theorem:** When a transversal cuts two parallel lines, alternate interior angles are congruent. 3. **Identify the angles:** $\angle 3$ and $\angle 6$ are alternate interior angles because they lie between the two parallel lines on opposite sides of the transversal. 4. **Apply the theorem:** Since $a \parallel b$, by the Alternate Interior Angles Theorem, $\angle 3 \cong \angle 6$. 5. **Conclusion:** Therefore, $\angle 3$ is congruent to $\angle 6$ as required.