\(a,\left\{{}\begin{matrix}AM=MD\\BN=NC\end{matrix}\right.\Rightarrow MN\) là đtb hthang ABCD
\(\Rightarrow MN=\dfrac{AB+CD}{2}\Rightarrow12=AB+8\Rightarrow AB=4\left(cm\right)\\ MN//AB//CD\)
\(b,\left\{{}\begin{matrix}MP//AB\\AM=MD\end{matrix}\right.\Rightarrow DP=PB\Rightarrow MP\) là đtb tam giác ABD
\(\Rightarrow MP=\dfrac{1}{2}AB=2\left(cm\right)\)
\(\left\{{}\begin{matrix}NQ//AB\\NB=NC\end{matrix}\right.\Rightarrow AQ=QC\Rightarrow NQ\) là đtb tam giác ABC
\(\Rightarrow NQ=\dfrac{1}{2}AB=2\left(cm\right)\\ \Rightarrow PQ=MN-NQ-MP=6-2-2=2\left(cm\right)\)
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