$\begin{array}{l}
SA \bot \left( {ABCD} \right) \Rightarrow SA \bot BC,BC \bot AB\\
 \bullet \left\{ \begin{array}{l}
SA \bot BC\\
BC \bot AB\\
SA \cap AB = \left\{ A \right\}
\end{array} \right. \Rightarrow BC \bot \left( {SAB} \right)\\
 \Rightarrow BC \bot AM \subset \left( {SAB} \right)\\
AM \bot SB\left( {gt} \right) \Rightarrow AM \bot \left( {SBC} \right)\\
tt:CD \bot \left( {SAD} \right) \Rightarrow CD \bot AN \subset \left( {SAD} \right)\\
AN \bot SD\left( {gt} \right) \Rightarrow AN \bot \left( {SCD} \right)\\
 \bullet AM \bot \left( {SBC} \right) \Rightarrow AM \bot SC\\
 \bullet AN \bot \left( {SCD} \right) \Rightarrow AN \bot SC\\
\left\{ \begin{array}{l}
SC \bot AM\\
SC \bot AN\\
AM \cap AN = \left\{ A \right\}
\end{array} \right. \Rightarrow SC \bot \left( {AMN} \right)
\end{array}$