1. **Problem statement:** Given triangle VYX with W and Z as midpoints of segments VX and VY respectively, and segment WZ = 10, find the length of XY. 2. **Key concept:** When W and Z are midpoints of two sides of a triangle, segment WZ is parallel to the third side XY and its length is half of XY (Midsegment Theorem). 3. **Formula:** $$WZ = \frac{1}{2} XY$$ 4. **Given:** $$WZ = 10$$ 5. **Find:** $$XY$$ 6. **Calculation:** Using the formula, $$10 = \frac{1}{2} XY$$ Multiply both sides by 2: $$XY = 2 \times 10 = 20$$ 7. **Answer:** The length of segment XY is $$20$$.