题目
题型:不详难度:来源:
![](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)
答案
解析
试题分析:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052132-24611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052133-60724.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052133-84873.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052133-90552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052133-42200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052131-10286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052133-34272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052134-29062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052134-57945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052134-50512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052134-49831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052132-62682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052134-20893.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052132-62682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052135-72641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052132-62682.png)
(Ⅱ) 解法1:证明:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052135-25049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052130-74105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052135-84303.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052130-74105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052135-60580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052135-48582.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052136-96952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052136-34686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052136-15541.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052136-34686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052136-77145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052136-11075.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052129-22648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052136-62876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052137-22098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052136-34686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052137-48192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052136-34686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052137-67221.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052137-22385.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052137-12479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052138-95512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052138-75068.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052138-89235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052138-39714.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052138-89679.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052139-49959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052139-24587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052139-80232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052139-24587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052139-82160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052139-24587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052139-48860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052139-24587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052132-86755.png)
解法2:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052135-25049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052130-74105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052135-84303.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052130-74105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052140-99294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052130-74105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052135-60580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052140-40106.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052140-89372.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052130-66958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052140-49126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052141-50999.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052140-49126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052141-62013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052141-64175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052141-35303.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052142-22594.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052142-12757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052142-32256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052142-47281.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052142-18298.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052132-86755.png)
(Ⅲ)由已知得
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052143-99401.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052143-48357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052143-71175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052143-21500.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052143-86549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052144-38396.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052144-33885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052144-89029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052144-33909.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052144-98953.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052145-78264.png)
设二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052132-44201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052145-63623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052145-88633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052145-28224.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052145-78211.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052146-68865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052132-44201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052146-10384.png)
点评:
核心考点
举一反三
![](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)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052031-46773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052031-46210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052032-40946.jpg)
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