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خطا

$\overline{AD}=\overline{DE}\Rightarrow \hat{A}={{\hat{E}}_{1}}$ (1) $\begin{align}  & \left. \begin{matrix}   D:\overline{AD}=\overline{DC}  \\   \overline{AD}=\overline{DE}  \\\end{matrix} \right\}\Rightarrow \overline{DE}=\overline{DC} \\  & \Rightarrow \hat{C}={{{\hat{E}}}_{2}} \\ \end{align}$ $\begin{align}  & A\overset{\Delta }{\mathop{C}}\,E:{{\underbrace{\hat{A}+\hat{C}+{{{\hat{E}}}_{1}}+{{{\hat{E}}}_{2}}=180{}^\circ }_{{}}}_{{}}}\xrightarrow{(1),(2)}2{{{\hat{E}}}_{1}}+2{{{\hat{E}}}_{2}}=180 \\  & \Rightarrow {{{\hat{E}}}_{1}}+{{{\hat{E}}}_{2}}=90{}^\circ \Rightarrow A\hat{E}C=90{}^\circ  \\ \end{align}$