题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030539-87545.png)
(Ⅰ)求证:AG∥平面PEC;
(Ⅱ)求点G到平面PEC的距离.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030539-75490.png)
解析
试题分析:(Ⅰ)要证明一条直线和一个平面平行,只需在面内找一条直线与之平行,如果找不到,可将这条直线平移到平面内,取
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030539-52906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030540-97439.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030540-87600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030540-40289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030540-30364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030540-55267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030540-40289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030541-61841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030541-21053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030541-61841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030541-18120.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030541-32903.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-56939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-77107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-56939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-80442.png)
(Ⅱ)点到平面的距离指的是点到平面垂线段的长度,如果垂足不好确定,可考虑四面体的等体积转换,由(Ⅰ)知
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-56939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-80442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-29978.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-73192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-80442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-73192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-80442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030543-92245.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030543-99282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030543-92245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030543-33056.png)
试题解析:(Ⅰ)证明:取PC的中点F,连接GF,则
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030540-40289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030541-61841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030541-21053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030541-61841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030543-51951.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030544-99379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030544-93483.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030541-21053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-56939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-77107.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030544-80089.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-56939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-80442.png)
(Ⅱ)由
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-56939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-80442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-29978.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-73192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-80442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-73192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030542-80442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030543-92245.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030544-28197.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030545-94277.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030545-26721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030545-68847.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030545-63249.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030546-22984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030546-25255.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030546-50795.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030546-88475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030539-75490.png)
核心考点
试题【如图,在四棱锥P—ABCD中,PA⊥平面ABCD,四边形ABCD为正方形,PA=AB=4,G为PD的中点,E是AB的中点. (Ⅰ)求证:AG∥平面PEC; (】;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/20191106/20191106030522-54346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030522-65023.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030522-16270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030522-55199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030523-91327.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030523-14346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030523-42488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030523-19874.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030523-22257.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030523-10302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030510-19258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030510-71091.png)
①若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030511-99691.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030511-56781.png)
③若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030511-35556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030511-65804.png)
其中真命题的序号为( )
A.①② | B.②③ | C.③④ | D.①④ |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030503-36864.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030504-19868.png)
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() |
A.若直线![]() ![]() ![]() ![]() |
B.若四点不共面,则这四点中任意三点都不共线 |
C.若两条直线没有公共点,则这两条直线是异面直线 |
D.两条异面直线不可能垂直于同一个平面 |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030452-38399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030452-19903.png)
①若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030452-76188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030453-20381.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030453-15976.png)
②若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030452-76188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030453-40759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030453-33723.png)
③若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030454-62268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030454-32849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030454-90307.png)
④若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030454-33536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030455-92447.png)
其中正确的命题是( )
A.①② | B.②③ | C.②④ | D.①④ |
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