题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020100-12765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020100-97952.jpg)
(1)求证: EC⊥CD;
(2)求证:AG∥平面BDE;
(3)求:几何体EG-ABCD的体积.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020101-82423.png)
解析
试题分析:(1)要证
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020101-96865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020101-67682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020101-34200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020102-51783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020102-70571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020102-33686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020101-67682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020101-34200.png)
(2)过G作GN⊥CE交BE于M,连 DM,由题设可证四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020102-74022.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020103-62313.png)
从而由直线与平面平行的判定定理,可证AG∥平面BDE;
(3)欲求几何体EG-ABCD的体积,可先将该几何体分成一个四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020103-64430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020103-92829.png)
试题解析:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020103-42078.jpg)
(1)证明:由平面ABCD⊥平面BCEG,
平面ABCD∩平面BCEG=BC,
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020104-60398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020104-11310.png)
又CD
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020104-53146.png)
(2)证明:在平面BCDG中,过G作GN⊥CE交BE于M,连DM,则由已知知;MG=MN,MN∥BC∥DA,且
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020104-39133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020104-11310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020104-11310.png)
∵DM
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020104-88096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020105-34885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020104-11310.png)
(3)解:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020105-81526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020105-93176.png)
核心考点
试题【如图, 已知四边形ABCD和BCEG均为直角梯形,AD∥BC,CE∥BG,且,平面ABCD⊥平面BCEG,BC=CD=CE=2AD=2BG=2.(1)求证: E】;主要考察你对向量与空间位置关系等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020043-66152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020044-91728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020044-45367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020044-61540.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020044-66036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020044-48642.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020044-65528.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020044-31421.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020044-34912.png)
(3)在线段
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020044-83905.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020044-24024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020045-31037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020045-66992.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020044-31421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020045-94500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020022-63765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020022-68275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020023-49604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020023-20514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020023-45843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020024-88042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020024-15686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020024-39313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020024-98024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020024-75145.jpg)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020025-88023.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020023-45843.png)
(2)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020025-25885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020025-36957.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020025-97716.png)
(3)求四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020022-63765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020014-79245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020014-96080.png)
A.若![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020007-15059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020007-67995.png)
①
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020007-95286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020007-97452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020008-30353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020008-70754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020008-33239.png)
(1)当满足条件 时,有
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020008-21509.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020009-23127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020002-39159.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020002-14232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020003-62947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106020002-14232.png)
A.![]() ![]() | B.![]() ![]() | C.![]() ![]() | D.![]() ![]() |
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