题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053309-28216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053309-18925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053309-29262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053309-61896.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053310-87297.png)
(I) 证明: PA∥平面EDB;
(II) 证明:PB⊥平面EFD;
答案
(2)根据已知的线面垂直可知PD⊥底面ABCD且DC⊂底面ABCD,∴PD⊥DC
,同时可知同样由PD⊥底面ABCD,得PD⊥BC.进而推理得到BC⊥平面PDC.结合判定定理得到证明。
解析
试题分析:解:(1)证明:连接AC,AC交BD于O,连接EO.
∵底面ABCD是正方形,∴点O是AC的中点
在△PAC中,EO是中位线,∴PA∥EO
而EO⊂平面EDB且PA⊄平面EDB,
所以,PA∥平面EDB
(2)证明:
∵PD⊥底面ABCD且DC⊂底面ABCD,∴PD⊥DC
∵PD=DC,可知△PDC是等腰直角三角形,而DE是斜边PC的中线,
∴DE⊥PC.①
同样由PD⊥底面ABCD,得PD⊥BC.
∵底面ABCD是正方形,有DC⊥BC,∴BC⊥平面PDC.
而DE⊂平面PDC,∴BC⊥DE.②
由①和②推得DE⊥平面PBC
而PB⊂平面PBC,∴DE⊥PB
又EF⊥PB且DE∩EF=E,所以PB⊥平面EFD.
点评:本小题考查直线与平面平行,直线与平面垂直,二面角等基础知识,考查空间想象能力和推理论证能力
核心考点
试题【如图,在四棱锥中,底面ABCD是正方形,侧棱底面ABCD,,E是PC的中点,作交PB于点F.(I) 证明: PA∥平面EDB;(II) 证明:PB⊥平面EFD;】;主要考察你对线线角等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053301-38539.png)
(Ⅰ)证明PQ⊥平面ABCD;
(Ⅱ)求异面直线AQ与PB所成的角;
(Ⅲ)求点P到平面QAD的距离.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053250-76696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053251-83353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053251-89503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053251-16777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053251-50948.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053252-55014.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053252-97266.jpg)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053252-28471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053252-28030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053252-11578.png)
(Ⅱ)求点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053253-59256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053253-40615.png)
如图,在四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053238-37315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053238-23479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053239-42198.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053239-89122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053239-87888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053239-45373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053239-28057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053239-74544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053239-62349.png)
(1) 设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053240-71973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053240-10523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053240-20469.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053240-98725.png)
(2) 求四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053238-37315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053231-23721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053231-58591.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053231-20762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053232-93008.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053232-85969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053232-14137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053232-23775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053232-59756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053233-53556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053233-41951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053233-88456.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053233-55307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053234-63254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053234-61145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053234-92667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053220-94317.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053220-51326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053220-45979.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053220-78307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053220-80518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053221-82081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053221-68130.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053221-24602.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053221-76674.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053222-11419.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053222-97707.png)
(2)求截面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053222-97421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053220-45979.png)
(3)求点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053222-35507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022053222-97421.png)
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