1. **Problem Statement:** We have a right triangle $VXY$ with a right angle at $V$. Points $W$ and $Z$ are midpoints of segments $VX$ and $VY$ respectively. Given that $WZ = 10$, we need to find the length of $XY$. 2. **Key Concept:** The segment $WZ$ connecting the midpoints of two sides of a triangle is called a midsegment. The Midsegment Theorem states that this segment is parallel to the third side and its length is half the length of that side. 3. **Applying the Midsegment Theorem:** Since $W$ and $Z$ are midpoints of $VX$ and $VY$, segment $WZ$ is parallel to $XY$ and: $$WZ = \frac{1}{2} XY$$ 4. **Calculate $XY$:** Given $WZ = 10$, substitute into the formula: $$10 = \frac{1}{2} XY$$ Multiply both sides by 2: $$XY = 2 \times 10 = 20$$ 5. **Answer:** The length of $XY$ is $20$. This uses the property of midsegments in triangles, which is a fundamental concept in geometry.