Question

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Explanation:

Step1: Identify segment sum rule

By segment addition postulate, $AC = AB + BC$ and $XZ = XY + YZ$.

Step2: Substitute into inequality

Replace $AB + BC$ with $AC$ and $YZ + XY$ with $XZ$ in $AB + BC
eq YZ + XY$, getting $AC
eq XZ$.

Step3: Contradict given congruence

We are given $\overline{AC} \cong \overline{XZ}$, so $AC = XZ$, which contradicts $AC
eq XZ$. Thus our initial assumption is false.

Answer:

First dropdown: Segment Addition Postulate
Second dropdown: $AC = AB + BC$ and $XZ = XY + YZ$