1. **State the problem:** We are asked to determine if two triangles are similar and to give reasons for their similarity. 2. **Recall the similarity criteria for triangles:** - **AAA (Angle-Angle-Angle):** If all three angles of one triangle are equal to the corresponding angles of another triangle, the triangles are similar. - **SAS (Side-Angle-Side):** If two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, the triangles are similar. - **SSS (Side-Side-Side):** If all three sides of one triangle are proportional to the corresponding sides of another triangle, the triangles are similar. 3. **Analyze the first pair of triangles (Triangle ABC and Triangle DEF):** - Given angles: ∠A = 112°, ∠B = 33°, ∠C = 35° for ABC - Given angles: ∠D = 112°, ∠E = 33°, ∠F = 35° for DEF - Since all corresponding angles are equal, by the AAA criterion, the triangles are similar. 4. **Analyze the second pair of triangles (Triangle ABC and Triangle XYZ):** - Triangle ABC has sides AB = 5, BC = 3, and a right angle at B (∠B = 90°). - Triangle XYZ has sides XZ = 15, YZ = 9, and a right angle at Z (∠Z = 90°). - Check if the sides are proportional: $$\frac{AB}{XZ} = \frac{5}{15} = \frac{1}{3}$$ $$\frac{BC}{YZ} = \frac{3}{9} = \frac{1}{3}$$ - The included angles are both right angles (90°). - By the SAS criterion, since two sides are proportional and the included angle is equal, the triangles are similar. **Final answers:** - Triangles ABC and DEF are similar by AAA. - Triangles ABC and XYZ are similar by SAS.