Question

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∥平面aec

Answer 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

Answer 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

Answer 3

My Mother
My mother is a kind woman.She is 35 years old.She is tall.She has two big eyes.She is a good teacher.She teaches English.She goes work at 7 o'clock.She goes home at 6 o'clock.She likes reading book.On Saturday,she often does housework.Sometimes she does sports.She is a good mother.I love my mother.