题目
题型:不详难度:来源:
如图,在多面体
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022019-63548.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022020-26677.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022020-50396.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022020-89076.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022020-68816.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022021-75910.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022021-61942.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022021-59483.gif)
(1)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022021-20549.gif)
(2)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022021-64625.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022022-11568.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022022-75518.jpg)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022022-85008.gif)
(2)略
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022022-26029.gif)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022023-31803.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022023-26602.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022023-65382.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022023-64086.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022023-78125.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022023-64086.gif)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022024-22189.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022023-64086.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022024-19797.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022024-50678.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022021-20549.gif)
由题意知:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022024-95222.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022025-59341.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022025-63594.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022025-59341.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022025-53137.gif)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022025-24523.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022026-19918.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022026-57207.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022026-91473.gif)
即:二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022021-20549.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022022-85008.gif)
(2)证明:令AC与BD交点为O,取BC中点H,连接HO,OE,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022026-51579.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022026-20756.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022027-18150.gif)
又EF//AB,AB=2EF,
则EOHF为平行四边形,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022026-20756.gif)
而BF=FC,H是BC的中点
则:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022027-91976.gif)
另一方面,由EF//AB,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022027-99832.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022027-76966.gif)
又ABCD为正方形,得:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022028-67886.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022028-61774.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022026-20756.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022028-36450.gif)
而FH
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022028-78436.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022028-26400.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022028-26400.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022029-38019.gif)
而:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022029-53954.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022022-11568.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022029-11409.gif)
由(1)(2)(3)可得:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022029-54048.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022022-11568.gif)
而:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022030-75757.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022030-28011.gif)
所以:面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022021-64625.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022022-11568.gif)
核心考点
试题【(本小题10分)如图,在多面体中,四边形是正方形,∥,,,,.(1)求二面角的正切值;(2)求证:平面平面.】;主要考察你对空间几何体的结构特征等知识点的理解。[详细]
举一反三
如图,正方形ABCD和四边形ACEF所在的平面互相垂直. EF//AC,AB=
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022007-95804.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022008-29733.gif)
(1)求证:AF//平面BDE;
(2)求异面直线AB与DE所成角的余弦值.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022008-34076.jpg)
如图,在多面体ABCDEF中,四边形ABCD是正方形,AB=2EF=2,EF∥AB,EF⊥FB,∠BFC=90°,BF=FC.
(1)求证:平面ABFE⊥平面DCFE;
(2)求四面体B—DEF的体积.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021955-68800.jpg)
如图,三棱锥P-ABC中,PA⊥底面ABC,AB⊥BC,DE垂直平分PC,且分别交AC、PC于D、E两点,又PB=BC,PA="A" B.
(Ⅰ)求证:PC⊥平面BDE;
(Ⅱ)若点Q是线段PA上任一点,求证:BD⊥DQ;
(Ⅲ)求线段PA上点Q的位置,使得PC//平面BDQ.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021951-62634.jpg)
如图,在长方体
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021940-62568.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021940-73049.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021940-61406.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021940-87877.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021941-44216.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021941-30991.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021941-30392.gif)
(1)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021941-13942.gif)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021941-95054.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021942-91753.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021942-26730.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021935-10297.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021935-87552.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021935-88437.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021936-75937.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021935-87552.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021936-79160.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021936-68444.gif)
A.0条 | B.1条 | C.2条 | D.无数条 |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021936-25959.jpg)
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