题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230643-30156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230643-58060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230643-61503.png)
(Ⅰ)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230643-25317.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230644-33894.png)
(Ⅱ)若直线PC与平面PDE所成角为
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230644-11094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230644-14086.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230644-46171.jpg)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230645-92528.png)
解析
试题分析:(Ⅰ)由线线垂直得到线面垂直CD⊥平面PAC,进而求证出面面垂直;(Ⅱ)由已知条件求出S△PCD和S△BCD,再利用等体积法求出三棱锥B-PCD的高.
试题解析:(Ⅰ)在正六边形ABCDEF中,CD⊥AC.
因为PA⊥底面ABCDEF,CDÌ平面ABCDEF,所以CD⊥PA.
又AC∩PA=A,所以CD⊥平面PAC.
因为CDÌ平面PCD,所以平面PAC⊥平面PCD.
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230645-70828.png)
(Ⅱ)直线PC与底面ABCDEF所成的角∠PCA=45°.
在Rt△PAC中,AC=
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230645-92528.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230645-92528.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230645-47686.png)
即三棱锥P-BCD的高为
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230645-92528.png)
S△PCD=
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230645-11677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230645-51279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230645-11677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230646-12358.png)
设三棱锥B-PCD高为h,由VP-BCD=VB-PCD,得:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230646-84234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230646-84234.png)
经计算可得:h=
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230646-10028.png)
所以三棱锥B-PCD高为
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230646-10028.png)
核心考点
试题【如图,六棱锥的底面是边长为1的正六边形,底面。(Ⅰ)求证:平面平面;(Ⅱ)若直线PC与平面PDE所成角为,求三棱锥高的大小。】;主要考察你对空间几何体的结构特征等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230634-62455.png)
(Ⅰ) 求证:FG∥平面PDC;
(Ⅱ) 求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230634-50038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230611-29747.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230612-58178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230612-74466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230612-62757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230612-74466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230612-95204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230612-79818.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230613-57877.png)
(Ⅰ)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230613-89693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230613-47807.png)
(Ⅱ)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230613-88065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230552-15806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230553-77318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230553-55488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230553-64423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230553-92288.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230552-15806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230553-28345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230553-44012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230554-70484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230554-64779.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230554-76812.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230554-63537.png)
(Ⅱ)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230554-68364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230555-11170.png)
(Ⅲ)求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230555-10798.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230540-85236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230540-97329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230540-18043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230540-55179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230541-65437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230541-95543.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230541-34134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230541-54478.png)
(Ⅱ)求平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230541-54478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230540-85236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230542-47682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230526-24169.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230526-21278.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230526-92801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230527-13786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230527-41810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230527-12248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230527-43514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230528-69890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230528-16163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230528-84117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230528-89211.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230527-12248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230527-43514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230526-24169.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230529-75600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230529-86800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230529-39070.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230529-70338.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230530-20949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230530-27898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230530-15433.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230530-17904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230530-94599.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230531-28132.jpg)
(I)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230531-66983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230531-85085.png)
(Ⅱ)若二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230531-93087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230531-85990.png)
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