1. **State the problem:** We are given two similar triangles $\triangle STU$ and $\triangle FEG$ with angles and side lengths labeled. We need to complete the similarity statement and find the ratio of a side length in $\triangle STU$ to its corresponding side length in $\triangle FEG$. 2. **Identify corresponding angles:** Since the triangles are similar, their corresponding angles are equal. Given angles: $\angle S = 94^\circ$, $\angle T = 56^\circ$, $\angle U = 30^\circ$ and $\angle F = 94^\circ$, $\angle E = 56^\circ$, $\angle G = 30^\circ$. 3. **Match vertices for similarity:** Corresponding angles imply corresponding vertices: \[ \triangle STU \sim \triangle FEG \] 4. **Identify corresponding sides:** Corresponding sides are opposite corresponding angles: - Side $ST$ corresponds to side $FE$ - Side $TU$ corresponds to side $EG$ - Side $SU$ corresponds to side $FG$ 5. **Use given side lengths:** - $ST = 6$, $TU = 10$, $SU = 12$ - $FE = 15$, $EG = 25$, $FG = 30$ 6. **Calculate ratio of corresponding sides:** Choose any pair, for example $ST$ and $FE$: $$ \text{ratio} = \frac{ST}{FE} = \frac{6}{15} $$ 7. **Simplify the fraction:** $$ \frac{6}{15} = \frac{\cancel{3} \times 2}{\cancel{3} \times 5} = \frac{2}{5} $$ **Final answers:** - Similarity statement: $\triangle STU \sim \triangle FEG$ - Ratio of side lengths: $\frac{2}{5}$