smc

Points $A,B,C$, and $D$ are distinct and lie, in the given order, on a straight line. Line segments $AB,AC$, and $AD$ have lengths $x,y$, and $z$, respectively. If line segments $AB$ and $CD$ may be rotated about points $B$ and $C$, respectively, so that points $A$ and $D$ coincide, to form a triangle with positive area, then which of the following three inequalities must be satisfied? $$\begin{gathered} \text{I. }x<\frac{z}{2} \\ \text{II. }y<x+\frac{z}{2} \\ \text{III. }y<\frac{z}{2} \end{gathered}$$