1. **Problem statement:** Given a quadrilateral PQRS with parallel lines LM, SR, and PQ, and side lengths LM = 9 cm, PQ = 3 cm, and SR = 6 cm, find the ratio $\frac{LS}{PL}$. 2. **Understanding the problem:** Since LM, SR, and PQ are parallel, and LS is drawn parallel to PL, triangles formed are similar by the AA similarity criterion. This allows us to use ratios of corresponding sides. 3. **Key formula:** For similar triangles, corresponding sides are proportional: $$\frac{LS}{PL} = \frac{LM}{PQ}$$ 4. **Substitute known values:** $$\frac{LS}{PL} = \frac{9}{3}$$ 5. **Simplify the fraction:** $$\frac{LS}{PL} = \frac{\cancel{9}}{\cancel{3}} \times \frac{3}{1} = 3$$ 6. **Interpretation:** The ratio $\frac{LS}{PL}$ equals 3, meaning LS is three times the length of PL. **Final answer:** $$\boxed{\frac{LS}{PL} = 3}$$