如圖,
O是正方形ABC
D的中心,
PO
底面ABC
D,
E是
PC的中點。

求證:(Ⅰ)
PA∥平面B
DE;
(Ⅱ)平面
PAC

平面B
DE。
證明:(Ⅰ)連結(jié)EO,
在△PAC中,∵O是AC的中點,E是PC的中點,

∴OE∥AP
又∵OE

平面BDE,
PA

平面BDE,
∴PA∥平面BDE
(Ⅱ)∵PO

底面ABCD,
∴PO

BD
又∵AC

BD,且AC

PO=O,
∴BD

平面PAC.
而BD

平面BDE,
∴平面P

AC

平面BDE。
練習(xí)冊系列答案
相關(guān)習(xí)題
科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
四棱錐P—ABCD的所有側(cè)棱長都為

,底面ABCD是邊長為2的正方形,則CD與PA所成角的余弦值為( )
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
已知二面角

的大小為

,且

,則異面直線
m,n所成的角為( )
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
如圖,△
ABC是等腰直角三角形,
AC=
BC=
a,
P是△
ABC所在平面外一點,
PA=
PB=
PC=
a. (1)求證:平面
PAB⊥平面
ABC;(2)求
PC與△
ABC所在平面所成的角.

查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:填空題
如圖,矩形ABCD中,AB=1,BC=a,PA⊥平面ABCD,若在BC上只有一個點Q滿足PQ⊥DQ,則a的值等于 .
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
已知二面角

的平面角為

,點

在二面角內(nèi),

,

,

為垂足,且

設(shè)

到棱

的距離分別為

,當(dāng)

變化時,點

的軌跡方程是
查看答案和解析>>