1. **Problem statement:** We have two triangles WTV and TSV sharing vertex V and side TV. Given WT = 10, ST = 20, TU = 44, and VW \parallel SU, we need to find the length TV. 2. **Key concept:** Since VW is parallel to SU, triangles WTV and TSV are similar by the AA (Angle-Angle) similarity criterion. 3. **Similarity ratio:** The ratio of corresponding sides WT to ST is $ \frac{WT}{ST} = \frac{10}{20} = \frac{1}{2} $. 4. **Using similarity:** Corresponding sides TV and TU relate by the same ratio: $$ \frac{TV}{TU} = \frac{WT}{ST} = \frac{1}{2} $$ 5. **Calculate TV:** $$ TV = \frac{1}{2} \times TU = \frac{1}{2} \times 44 = 22 $$ 6. **Answer:** The length of TV is 22 units.