Question

show that the conjecture is false by providing a counterexample. if the length of $overline{xz}$ is 20 and point y lies on $overline{xz}$, then $xy = 10$ and $yz = 10$. counterexample: $xy=square$, $yz=square$

Explanation:

Step1: Consider non - mid - point case

If point $Y$ is not the mid - point of $\overline{XZ}$, the segment addition postulate states that $XY + YZ=XZ$. But we can find values where $XY
eq10$ and $YZ
eq10$ while $XZ = 20$.
Let $XY = 5$ and $YZ=15$. Here, $XZ=XY + YZ=5 + 15=20$, and $Y$ lies on $\overline{XZ}$, but $XY
eq10$ and $YZ
eq10$.

Answer:

$XY = 5$, $YZ = 15$