1. **State the problem:** We are given two similar triangles \(\triangle GHI\) and \(\triangle EDF\) with angles and side lengths labeled. We need to complete the similarity statement and find the ratio of a side length in \(\triangle GHI\) to its corresponding side length in \(\triangle EDF\). 2. **Identify corresponding angles:** Since the triangles are similar, their corresponding angles are equal. Given angles: \(\angle G = 59^\circ\), \(\angle H = 35^\circ\), \(\angle I = 86^\circ\) and \(\angle E = 59^\circ\), \(\angle D = 35^\circ\), \(\angle F = 86^\circ\). 3. **Write the similarity statement:** Match angles in order: \(G \leftrightarrow E\), \(H \leftrightarrow D\), \(I \leftrightarrow F\). So, \(\triangle GHI \sim \triangle EDF\). 4. **Identify corresponding sides:** Corresponding sides are opposite corresponding angles: - \(GH \leftrightarrow ED\) - \(HI \leftrightarrow DF\) - \(GI \leftrightarrow EF\) 5. **Use given side lengths:** From the problem, sides in \(\triangle GHI\) are 16, 28, 24 and in \(\triangle EDF\) are 4, 7, 6. We match sides by size and angle correspondence: - \(GH = 28\) corresponds to \(ED = 7\) - \(HI = 24\) corresponds to \(DF = 6\) - \(GI = 16\) corresponds to \(EF = 4\) 6. **Find the ratio of a side length in \(\triangle GHI\) to its corresponding side length in \(\triangle EDF\):** Calculate \(\frac{GH}{ED} = \frac{28}{7} = \cancel{\frac{28}{7}} = 4\) 7. **Simplify the ratio:** The ratio is \(4\), a whole number. **Final answers:** - Similarity statement: \(\triangle GHI \sim \triangle EDF\) - Ratio of corresponding sides: \(\frac{GH}{ED} = 4\)