1. **State the problem:** We are given two similar triangles PQR and DEF with corresponding sides. We need to find which ratio correctly describes the relationship between their corresponding sides. 2. **Identify corresponding sides:** Since triangles PQR and DEF are similar, their corresponding sides are proportional. Given: - PQ corresponds to DE - PR corresponds to DF - QR corresponds to EF (though QR's length is not given here) 3. **Check given side lengths:** - PQ = 4 cm, PR = 6 cm - DE = 6 cm, DF = 9 cm, EF = 6 cm 4. **Calculate ratios of corresponding sides:** - $\frac{PQ}{DE} = \frac{4}{6} = \frac{2}{3}$ - $\frac{PR}{DF} = \frac{6}{9} = \frac{2}{3}$ Both $\frac{PQ}{DE}$ and $\frac{PR}{DF}$ equal $\frac{2}{3}$, confirming similarity. 5. **Analyze each given option:** - $\frac{PQ}{DE} = \frac{4}{6}$ is correct and matches the calculated ratio $\frac{2}{3}$. - $\frac{PQ}{DE} = \frac{6}{4}$ is incorrect since it swaps numerator and denominator. - $\frac{PQ}{EF} = \frac{4}{9}$ is incorrect; EF corresponds to QR, not PQ. - $\frac{PR}{DE} = \frac{6}{6} = 1$ is incorrect because PR corresponds to DF, not DE. 6. **Final answer:** The correct relationship is $$\frac{PQ}{DE} = \frac{4}{6}$$ which simplifies to $\frac{2}{3}$ and matches the similarity ratio of the triangles.