题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030737-64199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030738-31416.jpg)
求证:(1)平面ADE⊥平面BCD;
(2)FB∥平面ADE.
答案
解析
试题分析:(1)首先根据直线与平民啊垂直的判定定理证明
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030738-95597.png)
然后再根据平面垂直的判定定理证明平面ADE⊥平面BCD;(2),取DC的中点N,首先证FN∥平面ADE,然后再证∴BN∥平面ADE,再根据平面与平民啊平行的判定定理证明∴平面ADE∥平面FNB,最后由面面平行的性质即可.
试题解析:(1)∵∆ADE是等边三角形,,M是DE的中点,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030738-13178.png)
∵在∆DMC中,DM=1,
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030737-64199.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030738-76344.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030739-16113.png)
在∆AMC中,
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030739-36163.png)
∴AM⊥MC,
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030739-24119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030739-62906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030738-95597.png)
∵AM
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030739-42181.png)
(2)取DC的中点N,连结FN,NB,
∵F,N分别是AC,DC的中点,∴FN∥AD,由因为FN
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030740-49907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030739-42181.png)
∵N是DC的中点,∴BC=NC=2,又
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030737-64199.png)
由BN
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030740-49907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030739-42181.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030740-74526.png)
∵FB
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030739-42181.png)
核心考点
试题【如图,在四棱锥A-BCDE中,侧面∆ADE是等边三角形,底面BCDE是等腰梯形,且CD∥BE,DE=2,CD=4, ,M是DE的中点,F是AC的中点,且AC=4】;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/20191106/20191106030730-75953.png)
(1)若PA=2,求直线AE与PB所成角的余弦值;
(2)若PA
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030730-55421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030715-38876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030716-18672.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030716-66988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030716-47339.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030716-66657.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030715-38876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030716-96439.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030716-44566.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030716-63989.png)
⑴求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030716-93956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030716-46455.png)
⑵求平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030717-48478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030715-38876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030703-66788.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030703-93430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030704-39706.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030657-11206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030657-97038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030657-58388.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030657-97038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030657-58388.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030657-11206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030657-46175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030657-46264.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030657-39130.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030658-37857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030657-46175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030657-46264.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030658-38537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030657-97038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030657-58388.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030657-46175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030657-46264.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030658-38537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030657-97038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030657-58388.png)
A.4个 | B.3个 | C.2个 | D. 1 |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030648-85239.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030648-65997.png)
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