1. **State the problem:** We have a large right triangle VYX and a smaller triangle WZX inside it. W is the midpoint of VX, and Z is the midpoint of VY. Given that the length WZ = 10, we need to find the length XY. 2. **Recall midpoint and segment properties:** The midpoint of a segment divides it into two equal parts. Since W and Z are midpoints of VX and VY respectively, segments VW = WX and VZ = ZY. 3. **Use the Midsegment Theorem:** In a triangle, the segment connecting the midpoints of two sides is parallel to the third side and half its length. Here, WZ connects midpoints W and Z of sides VX and VY, so WZ is parallel to XY and $$WZ = \frac{1}{2} XY$$ 4. **Calculate XY:** Given that $$WZ = 10$$ Using the theorem, $$10 = \frac{1}{2} XY \implies XY = 2 \times 10 = 20$$ 5. **Answer:** The length of XY is 20.