cho hình chóp $SABCD$ đấy là hình bình hành.gọi $M,N,P,Q$ lần lượt là các điểm thuộc $BC,SC,SD,AD$..sao cho         $ MN//BS, NP//CD, MQ//CD$
a.CMR$:$ $PQ//SA$
b.gọi $K=MN \cap  PQ$.  CMR .$K\in$ đường thẳng cố định khi $M$ chạy trên $BC$
b, ta có (SBC) $\cap $ (SAD)=Sx , Sx //AD//BC
$(SBC)\supset MN\cap PQ\subset (SAD)=K(1)$
mà  $(SBC)\cap (SAD)=Sx(2)$
từ $(1)và(2) =>K\in Sx   $ cố định khi $M$ chạy trên $BC$
a, xét tam giác SBC có MN //SB => $\frac{BM}{BC}=\frac{SN}{SC}(1)$
xét tam giác SCD có NP//CD =>$\frac{SN}{SC}=\frac{SP}{SD}(2)$
xét hbh ABCD có AB//MQ//CD=>$\frac{BM}{BC}=\frac{AQ}{AD}(3)$
từ (1)(2)(3) => $\frac{AQ}{AD}=\frac{SP}{SD}$
xét tam giác SAD  có $\frac{AQ}{AD}=\frac{SP}{SD}=>SA//PQ$

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