1. **Problem Statement:** We are given two similar triangles and need to identify which triangles are similar and then solve for the missing side lengths. 2. **Formula and Rules:** For similar triangles, corresponding sides are proportional. If triangles ABC and DEF are similar, then: $$\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}$$ This means the ratios of corresponding sides are equal. 3. **Identify Similar Triangles:** Since the problem states the triangles are similar, we label them as $\triangle ABC \sim \triangle DEF$. 4. **Set up Proportions:** Suppose we know some side lengths and want to find a missing side, say $x$. For example, if $AB = 6$, $DE = 3$, and $BC = x$, $EF = 4$, then: $$\frac{AB}{DE} = \frac{BC}{EF} \Rightarrow \frac{6}{3} = \frac{x}{4}$$ 5. **Solve for the Missing Side:** Cross multiply: $$6 \times 4 = 3 \times x$$ $$24 = 3x$$ 6. **Simplify:** $$x = \frac{24}{3}$$ 7. **Cancel common factors:** $$x = \frac{\cancel{24}^{8} \times 3}{\cancel{3}} = 8$$ 8. **Answer:** The missing side length $x$ is 8. This method applies to any missing side in similar triangles by setting up the correct proportion and solving for the unknown.