1. **State the problem:** Determine if triangles TUS and GIH are similar. 2. **Recall similarity criteria:** Triangles are similar if their corresponding angles are equal or their corresponding sides are in proportion. 3. **Check angles:** - Triangle TUS angles: 32°, 59°, 89° - Triangle GIH angles: 59°, 86°, 35° No pair of triangles have all three angles equal. For example, 32° ≠ 35°, 89° ≠ 86°. 4. **Check sides ratios:** - Triangle TUS sides: UT=28, TS=24, US=15 - Triangle GIH sides: IG=12, IH=18, GH=21 Calculate ratios of corresponding sides assuming order UT-IG, TS-IH, US-GH: $$\frac{28}{12} = 2.33, \quad \frac{24}{18} = 1.33, \quad \frac{15}{21} = 0.71$$ Since these ratios are not equal, sides are not proportional. 5. **Conclusion:** Triangles TUS and GIH are not similar because neither their angles match nor their sides are proportional.