1. **State the problem:** We have two triangles with a pair of parallel sides: TU is parallel to QR. Given QR = 15, TU = 10, and QS = 9, we need to find the length of TS. 2. **Use the properties of parallel lines and similar triangles:** Since TU is parallel to QR, triangles TUS and QRS are similar by the AA (Angle-Angle) similarity criterion. 3. **Set up the ratio of corresponding sides:** The ratio of sides in similar triangles is equal. So, $$\frac{TU}{QR} = \frac{TS}{QS}$$ 4. **Substitute the known values:** $$\frac{10}{15} = \frac{TS}{9}$$ 5. **Solve for TS:** Multiply both sides by 9: $$9 \times \frac{10}{15} = TS$$ Simplify the fraction: $$9 \times \frac{\cancel{10}}{\cancel{15}} = 9 \times \frac{2}{3} = 6$$ So, $$TS = 6$$ 6. **Answer:** The length of TS is 6. This matches the computation hint given.