1. **State the problem:** We need to determine if triangles ABC and DEF are similar. 2. **Recall the similarity criteria:** Triangles are similar if their corresponding angles are equal or if their corresponding sides are in proportion. 3. **List the given side lengths:** - Triangle ABC: AB = 9, BC = 6, AC = 12 - Triangle DEF: DE = 12, EF = 8, DF = 16 4. **Check side ratios:** Calculate the ratios of corresponding sides: - \( \frac{AB}{DE} = \frac{9}{12} = 0.75 \) - \( \frac{BC}{EF} = \frac{6}{8} = 0.75 \) - \( \frac{AC}{DF} = \frac{12}{16} = 0.75 \) 5. **Interpretation:** Since all three pairs of corresponding sides have the same ratio \(0.75\), the triangles have proportional sides. 6. **Conclusion:** Because the corresponding sides are proportional, triangles ABC and DEF are similar by the Side-Side-Side (SSS) similarity criterion. **Final answer:** Yes, the triangles are similar because their corresponding sides are in proportion with ratio \(0.75\).