1. **Problem Statement:** Determine if triangles ABC and DEF are similar given some side lengths and angles, and if possible, find the length of side EF. 2. **Similarity Criteria:** Two triangles are similar if their corresponding angles are equal or if their corresponding sides are in proportion (AA, SAS, or SSS similarity criteria). 3. **Given Data:** - Triangle ABC: AB = 9, BC = 6, AC = 10.8 (calculated), angles A = 60°, B = 100°, C = 20°. - Triangle DEF: DE = 12, DF = 20, angles D = 60°, E = 100°, F = 20°, EF = ? 4. **Check Angle Correspondence:** - Both triangles have angles 60°, 100°, and 20°. - Since all corresponding angles are equal, triangles ABC and DEF are similar by the AA criterion. 5. **Find the scale factor:** - Compare sides corresponding to angle 60°: AB (9) corresponds to DE (12). - Scale factor from ABC to DEF is $\frac{12}{9} = \frac{4}{3}$. 6. **Find EF:** - Side BC (6) corresponds to EF. - Using scale factor: $EF = 6 \times \frac{4}{3} = 8$. 7. **Final answers:** - a. Yes, triangles ABC and DEF are similar because their corresponding angles are equal. - b. The length of EF is 8. $$\boxed{\text{EF} = 8}$$