خطا
$\left\{ \begin{matrix} {{\widehat{D}}_{1}}+{{\widehat{D}}_{2}}={{90}^{{}^\circ }} \\ {{\widehat{C}}_{1}}+{{\widehat{D}}_{2}}={{90}^{{}^\circ }} \\ \end{matrix}\Rightarrow {{\widehat{D}}_{1}}={{\widehat{C}}_{1}} \right.$ $\left\{ \begin{matrix} {{\widehat{C}}_{1}}={{\widehat{D}}_{1}} \\ \widehat{A}=\widehat{D}={{90}^{{}^\circ }} \\ \end{matrix} \right.\xrightarrow{(زز)}A\overset{\Delta }{\mathop{B}}\,D\sim D\overset{\Delta }{\mathop{A}}\,C$ $\Rightarrow \frac{AB}{AD}=\frac{AD}{CD}$ $\Rightarrow A{{D}^{2}}=AB\times CD$ $\Rightarrow A{{D}^{2}}=4\times 9=36$ $\Rightarrow AD=6$