题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030224-29041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030225-57033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030225-44004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030225-59515.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030225-37124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030225-24252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030226-50663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030226-45973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030226-26067.jpg)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030226-79617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030227-91998.png)
(Ⅱ)求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030227-46392.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030227-65466.png)
解析
试题分析:(Ⅰ)连接
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030227-42742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030227-42742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030228-55338.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030228-13462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030228-60583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030228-60583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030228-83546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030229-41481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030229-89004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030229-91268.png)
试题解析:
(Ⅰ)证明:连接
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030227-42742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030227-42742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030228-55338.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030228-13462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030228-60583.png)
∵ 四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030225-57033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030228-13462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030227-42742.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030225-37124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030225-24252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030228-60583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030228-83546.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030229-57782.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030230-97270.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030226-79617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030227-91998.png)
(Ⅱ)解:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030230-50519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030230-34479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030230-48198.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030230-36206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030230-34479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030231-93534.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030225-59515.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030231-46588.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030229-41481.png)
取
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030231-25125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030232-41912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030232-65630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030232-72159.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030229-89004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030232-75916.png)
设三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030227-46392.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030233-25145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030229-91268.png)
有
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030233-99283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030233-90169.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030202-55914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030202-44964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030203-18253.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030203-54377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030203-42259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030204-48838.jpg)
(Ⅰ)点
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030204-40230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030204-53326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030204-70777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030205-24982.png)
(Ⅱ)求平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030205-43171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030202-44964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030154-75066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030154-28663.jpg)
(Ⅰ)求证:EO⊥平面ABCD;
(Ⅱ)求点D到平面AEC的距离.
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030149-19757.png)
①若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030149-45607.png)
②
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030150-87337.png)
③
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030150-15996.png)
④
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030150-82349.png)
A.1 | B.2 | C.3 | D.4 |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030137-90920.png)
(Ⅰ)证明EF//平面A1CD;
(Ⅱ)证明平面A1CD⊥平面A1ABB1;
(Ⅲ)求直线BC与平面A1CD所成角的正弦值.
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030122-68150.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030122-57755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030122-77325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030122-17811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030123-99051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030123-52185.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030123-35111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030123-14161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030124-95271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030124-91055.png)
(Ⅰ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030124-22510.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030124-57993.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030125-59354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030125-66086.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030125-41742.png)
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