题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052150-98608.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052150-14048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052151-62500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052151-11813.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052151-73960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052151-50300.jpg)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052152-37821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052152-27886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052152-29776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052152-10448.png)
答案
(2)对于面面垂直的证明,要根据已知中的菱形的对角线垂直,以及
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052152-89631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052153-96153.png)
解析
试题分析:(1)证明:设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052153-78412.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052153-82226.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052153-15767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052152-37821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052152-27886.png)
(2)连接PO,因为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052151-62500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052154-54896.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052150-14048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052154-47279.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052154-44078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052153-96153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052154-13674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052153-96153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052154-75622.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052152-89631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052153-96153.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052155-26230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052152-27886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052152-29776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052153-96153.png)
点评:解决的关键是根据线面垂直和面面垂直的判定定理来证明,属于基础题。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052129-22648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052130-74105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052130-66958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052130-80192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052130-76389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052130-57335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052131-44953.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052131-47116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052131-14345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052131-10286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052131-64286.png)
(Ⅰ) 求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052132-38291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052132-62682.png)
(Ⅱ) 求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052132-86755.png)
(Ⅲ) 求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052132-44201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052116-75952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052116-83850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052116-42298.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052116-72340.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052116-76546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052116-92442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052116-46479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052117-46676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052117-44708.png)
(1)证明:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052117-94866.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052117-98945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052118-11640.png)
(2)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052118-60471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052118-40808.png)
已知:如图,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052108-49534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052108-68480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052109-63210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052109-15713.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052109-55287.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052109-82604.png)
已知一四棱锥P-ABCD的三视图如下,E是侧棱PC上的动点。
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052058-12148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052058-45351.png)
(Ⅰ)求四棱锥P-ABCD的体积;
(Ⅱ)当点E在何位置时,BD⊥AE?证明你的结论;
(Ⅲ)若点E为PC的中点,求二面角D-AE-B的大小.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052044-44268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052044-76840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052045-92258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052045-47202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052045-15888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052045-54449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052045-20463.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052045-65810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052045-58315.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052045-49238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052045-86165.png)
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