AHSME 1979 Problem 17

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? $\textbf{I. }x<\frac{z}{2} \\ \textbf{II. }y<x+\frac{z}{2} \\ \textbf{III. }y<\frac{z}{2}$

$\textbf{(A) }\textbf{I. }\text{only} \textbf{(B) }\textbf{II. }\text{only} \textbf{(C) }\textbf{I. }\text{and }\textbf{II. }\text{only} \textbf{(D) }\textbf{II. }\text{and }\textbf{III. }\text{only} \textbf{(E) }\textbf{I. },\textbf{II. },\text{and }\textbf{III. }$