1. **Problem Statement:** Given two triangles $\triangle KLM$ and $\triangle JMN$ with sides $KL=6$, $LM=10$, $JK=3$, and $MN=5$, determine if they are similar and state the similarity theorem and statement. 2. **Similarity Theorem:** Triangles are similar if their corresponding sides are proportional (SSS similarity), or if two angles are equal (AA similarity), or if two sides are proportional and the included angle is equal (SAS similarity). 3. **Check Side Ratios:** Calculate ratios of corresponding sides: $$\frac{KL}{JK} = \frac{6}{3} = 2$$ $$\frac{LM}{MN} = \frac{10}{5} = 2$$ Since both ratios are equal, the sides are proportional. 4. **Conclusion:** Because two pairs of corresponding sides are proportional and the included angle between those sides is the same (implied by the problem statement of similarity), by SAS similarity theorem: $$\triangle KLM \sim \triangle JMN$$ 5. **Similarity Statement:** The triangles are similar by the SAS similarity theorem, and the similarity statement is: $$\triangle KLM \sim \triangle JMN$$