1. **State the problem:** Determine if triangles $\triangle JKL$ and $\triangle MNP$ are similar, and if so, identify the correct similarity criterion. 2. **Given data:** - In $\triangle JKL$, sides: $KJ = 8$, $KL = 20$ - In $\triangle MNP$, sides: $NM = 6$, $NP = 15$ 3. **Similarity criteria:** - **AA (Angle-Angle):** Two triangles are similar if two pairs of corresponding angles are equal. - **SSS (Side-Side-Side):** Triangles are similar if all three pairs of corresponding sides are proportional. - **SAS (Side-Angle-Side):** Triangles are similar if two pairs of sides are proportional and the included angles are equal. 4. **Check side ratios:** Calculate ratios of corresponding sides: $$\frac{KJ}{NM} = \frac{8}{6} = \frac{4}{3} \approx 1.333$$ $$\frac{KL}{NP} = \frac{20}{15} = \frac{4}{3} \approx 1.333$$ Since two pairs of sides have the same ratio, check the third side to confirm SSS or SAS. 5. **Missing side lengths:** The problem does not provide the third side lengths $JL$ and $MP$, so we cannot verify SSS. 6. **Check angles:** No angle measures are given, so AA or SAS cannot be confirmed. 7. **Conclusion:** With only two pairs of sides proportional and no angle information, we cannot confirm similarity by SSS or SAS. Therefore, the triangles $\triangle JKL$ and $\triangle MNP$ are **not similar** based on the given information. **Final answer:** $\triangle JKL$ and $\triangle MNP$ are not similar.