1. **Problem Statement:** We are given triangle $\triangle VXZ$ with $WY$ as a midsegment. We know $VZ = p$ and $WY = p - 14$. We need to find the value of $p$. 2. **Key Concept:** A midsegment in a triangle connects the midpoints of two sides and is parallel to the third side. Importantly, the length of the midsegment is half the length of the third side. 3. **Formula:** If $WY$ is the midsegment parallel to $VZ$, then: $$WY = \frac{1}{2} VZ$$ 4. **Substitute the given values:** $$p - 14 = \frac{1}{2} p$$ 5. **Solve for $p$:** Multiply both sides by 2 to clear the fraction: $$2(p - 14) = p$$ $$2p - 28 = p$$ Subtract $p$ from both sides: $$2p - p = 28$$ $$p = 28$$ 6. **Answer:** The value of $p$ is $28$. This means the side $VZ$ measures 28 units, and the midsegment $WY$ measures $28 - 14 = 14$ units, which is half of $VZ$, confirming the property of the midsegment.