1. **State the problem:** Given that $MN \parallel JK$, prove that $\triangle JKL \sim \triangle MNL$.
2. **Identify the statements and reasons:**
| Statements | Reasons |
|---------------------|--------------------------------|
| 1. $MN \parallel JK$ | 1. Given |
| 2. $\angle LMN \cong \angle LJK$ | 2. Alternate Interior Angles Congruent |
| 3. $\angle L \cong \angle L$ | 3. Reflexive Property |
| 4. $\triangle JKL \sim \triangle MNL$ | 4. AA~ (Angle-Angle similarity) |
3. **Explanation:**
- Since $MN$ is parallel to $JK$, the angles $\angle LMN$ and $\angle LJK$ are alternate interior angles, so they are congruent.
- The angle $\angle L$ is common to both triangles, so by the Reflexive Property, it is congruent to itself.
- With two pairs of corresponding angles congruent, by the AA~ similarity criterion, the triangles $\triangle JKL$ and $\triangle MNL$ are similar.
**Final answer:**
| Statements | Reasons |
|---------------------|--------------------------------|
| 1. $MN \parallel JK$ | 1. Given |
| 2. $\angle LMN \cong \angle LJK$ | 2. Alternate Interior Angles Congruent |
| 3. $\angle L \cong \angle L$ | 3. Reflexive Property |
| 4. $\triangle JKL \sim \triangle MNL$ | 4. AA~ |
Triangle Similarity 5B6B33
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.