1. **State the problem:** Determine which triangles are similar to triangle $\triangle ABC$ with sides $3$, $7$, and $7$. 2. **Recall similarity criteria:** Triangles are similar if their corresponding sides are in proportion. 3. **Analyze $\triangle ABC$:** Sides are $3$, $7$, and $7$. The ratio of the two equal sides to the third is $\frac{7}{3} \approx 2.33$. 4. **Check $\triangle DFE$:** Sides are $5$, $5$, and $6$. - Ratios compared to $\triangle ABC$ sides: - $\frac{5}{3} \approx 1.67$ - $\frac{5}{7} \approx 0.71$ - $\frac{6}{7} \approx 0.86$ - These ratios are not consistent with $\triangle ABC$ side ratios. 5. **Check $\triangle HIG$:** Sides are $9$, $9$, and $5$. - Ratios compared to $\triangle ABC$ sides: - $\frac{9}{7} \approx 1.29$ - $\frac{9}{7} \approx 1.29$ - $\frac{5}{3} \approx 1.67$ - These ratios are not consistent with $\triangle ABC$ side ratios. 6. **Conclusion:** Neither $\triangle DFE$ nor $\triangle HIG$ have side lengths proportional to $\triangle ABC$. **Final answer:** Neither triangle is similar to $\triangle ABC$.