$\begin{array}{l}
\left( {A'CD} \right) \cap \left( {ABCD} \right) = CD\\
AB \cap CD = \left\{ E \right\}\\
\Rightarrow E \in AB \subset \left( {SAB} \right)\\
E \in CD \subset \left( {A'CD} \right)\\
\Rightarrow \left( {A'CD} \right) \cap \left( {SAB} \right) = A'E\\
\Rightarrow E \in CD \Rightarrow \left( {A'ED} \right) \equiv \left( {A'CD} \right)\\
A'E \cap BC = \left\{ F \right\}\\
\left( {A'CD} \right) \cap \left( {SBC} \right) = CF\\
\left( {SDA} \right) \cap \left( {A'CD} \right) = A'D
\end{array}$
