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牛顿定理的定理1证明

2025-03-17 11:51:11

推荐回答（1个）

回答1：

四边形ABCD,AB∩CD=E,AD∩BC=F,BD中点M,AC中点L,EF中点N
证明：
取BE中点P,BC中点R,PN∩CE=QR,L,Q共线
QL/LR=EA/AB
M,R,P共线
RM/MP=CD/DE
N,P,Q共线
PN/NQ=BF/FC
三式相乘得:
QL/LR*RM/MP*PN/NQ=EA/AB*CD/DE*BF/FC
由梅涅劳斯定理
QL/LR*RM/MP*PN/NQ=1
由梅涅劳斯定理的逆定理知:L,M,N三点共线
证毕
故牛顿定理1成立

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