1. **State the problem:** We are given triangle $\triangle ABC$ with sides $AB=0.9$, $BC=1$, and $AC=1.5$. We need to determine which of the given triangles $\triangle DEF$ or $\triangle GHI$ are similar to $\triangle ABC$. 2. **Recall the similarity rule for triangles:** Two triangles are similar if their corresponding sides are in proportion, i.e., the ratios of the lengths of their corresponding sides are equal. 3. **Calculate the side ratios of $\triangle ABC$:** $$\frac{AB}{BC} = \frac{0.9}{1} = 0.9, \quad \frac{BC}{AC} = \frac{1}{1.5} = \frac{2}{3} \approx 0.6667, \quad \frac{AB}{AC} = \frac{0.9}{1.5} = 0.6$$ 4. **Check similarity with $\triangle DEF$ (sides $DE=4.5$, $EF=5$, $DF=7.5$):** Calculate ratios: $$\frac{DE}{EF} = \frac{4.5}{5} = 0.9, \quad \frac{EF}{DF} = \frac{5}{7.5} = \frac{2}{3} \approx 0.6667, \quad \frac{DE}{DF} = \frac{4.5}{7.5} = 0.6$$ These ratios exactly match those of $\triangle ABC$. 5. **Check similarity with $\triangle GHI$ (sides $GH=3$, $HI=9$, $GI=10$):** Calculate ratios: $$\frac{GH}{HI} = \frac{3}{9} = \frac{1}{3} \approx 0.3333, \quad \frac{HI}{GI} = \frac{9}{10} = 0.9, \quad \frac{GH}{GI} = \frac{3}{10} = 0.3$$ These ratios do not match those of $\triangle ABC$. 6. **Conclusion:** Only $\triangle DEF$ has side ratios proportional to $\triangle ABC$, so only $\triangle DEF$ is similar to $\triangle ABC$. **Final answer:** $\triangle DEF$ only