1) \(MN\subset(MNC)\)
Trong mặt phẳng (ABC): \(CM\cap AB=I\Rightarrow I\in(MNC)\cap(ABD)\)
Trong mặt phẳng (ADC): \(CN\cap BD=J\Rightarrow J\in(MNC)\cap(ABD)\)
\(\Rightarrow IJ\in(MNC)\cap(ABD)\)
\(MN\cap(ABD)=MN\cap IJ=E\).
2) \(MN\subset(MNB)\)
Trong mặt phẳng (ABC): \(BM\cap AC=H\Rightarrow H\in(MNB)\cap(ACD)\)
Trong mặt phẳng (ADC): \(BN\cap CD=K\Rightarrow K\in(MNB)\cap(ACD)\)
\(\Rightarrow HK\in(MNB)\cap(ACD)\)
\(MN\cap(ACD)=MN\cap HK=F\).