$$\eqalign{
& VD4: \cr
& a)\,\,Trong\,\,\left( {ABCD} \right)\,\,goi\,\,E = BN \cap AD \cr
& \Rightarrow \left\{ \matrix{
E \in BN \hfill \cr
E \in AD \hfill \cr} \right. \Rightarrow E \in \left( {BMN} \right) \cap \left( {SAD} \right) \cr
& S \in \left( {BMN} \right) \cap \left( {SAD} \right) \cr
& \Rightarrow \left( {BMN} \right) \cap \left( {SAD} \right) = SE. \cr
& b)\,\,AD//BC \cr
& \Rightarrow Ap\,\,dung\,\,DL\,Ta - let: \cr
& {{NC} \over {NA}} = {{BN} \over {NE}} = {{BM} \over {MS}} = k \cr
& \Rightarrow MN//SE\,\,\left( {Dinh\,\,li\,\,Ta - let\,\,dao} \right) \cr
& Ma\,\,SE \subset \left( {SAD} \right) \cr
& \Rightarrow MN//\left( {SAD} \right) \cr
& c)\,\,Trong\,\,\left( {SDM} \right)\,\,ke\,\,GF//SE\,\,\left( {F \in \left( {EM} \right)} \right) \cr
& Ta\,\,co:\,\,{{MF} \over {ME}} = {{MG} \over {MS}} = {1 \over 3} \Rightarrow {{EF} \over {EM}} = {2 \over 3} \cr
& De\,\,\left( {GMN} \right)//\left( {SAD} \right) \Rightarrow NF//AD//BC \cr
& Keo\,\,dai\,\,ME\,\,cat\,\,BC\,\,tai\,\,H \cr
& Ta\,\,co:\,\,{{ME} \over {MH}} = {{MD} \over {MC}} = 1 \cr
& \Rightarrow ME = MH \cr
& \Rightarrow {{EF} \over {EH}} = {2 \over 3}.{1 \over 2} = {1 \over 3} = {{NE} \over {EB}} \cr
& Ta\,\,co:\,\,{{NC} \over {NA}} = {{NB} \over {NE}} = k \Rightarrow {{NB + NE} \over {NE}} = {{k + 1} \over 1} \cr
& \Rightarrow {{BE} \over {NE}} = k + 1 \Rightarrow {{NE} \over {BE}} = {1 \over {k + 1}} \cr
& \Rightarrow {1 \over 3} = {1 \over {k + 1}} \Rightarrow k = 2 \cr} $$
