题目
题型:不详难度:来源:
如图,在四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-73117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-27783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-18789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-41488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-41593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052242-58546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052242-90247.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052242-67139.png)
(Ⅰ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052242-93201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052242-65596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052242-30683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052242-67645.png)
(Ⅱ)求四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-73117.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052243-80171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052243-17144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-27783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-18789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052243-60364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052243-88525.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052244-71094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-18789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052244-83280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052242-67645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052244-71094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052244-10216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052242-30683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052242-67645.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052244-86561.png)
解析
试题分析:(Ⅰ)由于
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052244-50005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052245-25266.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052245-48446.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052243-80171.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052243-17144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052245-72177.png)
又平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-27783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-18789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052243-60364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052243-88525.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052244-71094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-18789.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052244-83280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052242-67645.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052244-71094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052244-10216.png)
故平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052242-30683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052242-67645.png)
(Ⅱ)解:过
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052245-53347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052246-67854.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052246-19150.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052246-81119.png)
由于平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-27783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-18789.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052246-86038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-18789.png)
因此
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052247-64734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-73117.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-41593.png)
因此
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052247-54808.png)
在底面四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-18789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-41488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052247-59156.png)
所以四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-18789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052247-82518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052247-63597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052248-90644.png)
此即为梯形
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-18789.png)
所以四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052241-18789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052248-24111.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052248-22144.png)
点评:立体几何问题主要是探求和证明空间几何体中的平行和垂直关系以及空间角、体积等计算问题.对于平行和垂直问题的证明或探求,其关键是把线线、线面、面面之间的关系进行灵活的转化.在寻找解题思路时,不妨采用分析法,从要求证的结论逐步逆推到已知条件
核心考点
举一反三
如图,四棱锥P—ABCD中,PA⊥底面ABCD,AB⊥AD,AC⊥CD,∠ABC=60°,PA=AB=BC,E是PC的中点。
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052237-43721.png)
(1)求证:CD⊥AE;
(2)求证:PD⊥面ABE。
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052229-71359.png)
(1) 求证:CE∥平面PAB;
(2) 求PA与平面ACE所成角的大小;
(3) 求二面角E-AC-D的大小.
如图,已知三棱锥A-BPC中,AP⊥PC,AC⊥BC,M为AB中点,D为PB中点,且△PMB为正三角形.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052221-55747.png)
(1)求证:DM∥平面APC;
(2)求证:平面ABC⊥平面APC;
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052218-23536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052218-89445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052218-75399.png)
①若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052219-87493.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052219-81973.png)
A.①是真命题,②是假命题 | B.①是假命题,②是真命题 |
C.①、②都是真命题 | D.①、②都是假命题 |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052208-16145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052208-29240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052208-81563.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052208-39801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052209-78270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052209-76953.png)
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