Gọi $E$ là trung điểm $CD$
$E\in SN;\, SN\subset(SMN)\Rightarrow E \in (SMN)$
$E\in CD;\, CD\subset (ABCD)\Rightarrow E \in (ABCD)$
$\Rightarrow (SMN)\cap (ABCD)=\left\{E\right\}$
Ta lại có:
$(SMN)\cap (ABCD)=\left\{A\right\}$
$\Rightarrow (SMN)\cap (ABCD)=AE$
$\Rightarrow (SMN)\subset (SAE)$
$\Rightarrow MN\subset (SAE)$
Trong $mp(SAE)$ gọi $MN\cap AE = \left\{F\right\}$
$F\in AE;\, AE\subset (ABCD)\Rightarrow F \in (ABCD)$
mà $F\in MN$
$\Rightarrow MN\cap (ABCD) = \left\{F\right\}$