1. **Problem Statement:** Given that angles $\angle 1 \cong \angle 2$, determine which lines are parallel among $a$, $b$, $c$, and $d$. 2. **Relevant Property:** When two corresponding angles are congruent, the lines that form these angles with a transversal are parallel. 3. **Analysis:** - Angles $\angle 1$ and $\angle 2$ are congruent. - These angles are formed by lines $a$ and $b$ intersected by the transversal lines $c$ and $d$. 4. **Conclusion:** Since $\angle 1 \cong \angle 2$ and they are corresponding angles, lines $a$ and $b$ are parallel. 5. **Answer:** $a \parallel b$.