13问答网 > 在底面为平行四边形的四棱锥p－abcd中，ab⊥ac，pa⊥平面abcd，点e是pd的中点。1求证ac⊥pb.2求证pb∥...

在底面为平行四边形的四棱锥p－abcd中，ab⊥ac，pa⊥平面abcd，点e是pd的中点。1求证ac⊥pb.2求证pb∥...

2025-05-11 20:03:14

推荐回答（3个）

回答1：

（1）∵pa⊥平面abcd,ac在平面abcd内、
∴pa⊥ac
∴ac⊥平面pab,∵pb属于平面pab
∴ac⊥pb

（2）连接bd交ac与o,连接eo
∵o、e分别为bd,pd的中点，∴在△pbd中、eo∥pb
∵eo属于平面aec
∴pb∥平面aec

回答2：

记AC与BD交点为O，设AO=x，BO=y，
则梯形面积为1/2(AO*BO+BO*CO+CO*DO+DO*AO)=1/2(xy+y(5-x)+(5-x)(4-y)+(4-y)x)
=1/2(xy+5y-xy+20-5y-4x+xy+4x-xy)=1/2*20=10

回答3：

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