题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024105-29379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024105-45475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024105-51040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024106-96048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024106-56076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024106-88378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024106-94590.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024107-75751.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024107-25968.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024107-71144.png)
(3)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024107-28078.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024108-65374.png)
解析
试题分析:(1)根据已有中点,
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024108-26130.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024108-93111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024108-60251.png)
(2)根据
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024109-37660.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024109-77061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024109-82690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024108-60251.png)
上述两小题,关键是要注意表述的规范性.
(3)解答本小题可利用“几何法”、“向量法”,应用“几何法”,要注意做好“作图,证明,计算”等工作.利用“向量法”,则要注意计算准确.
试题解析:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024109-92756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024110-27626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024108-93111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024108-60251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024110-21484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024110-42734.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024109-37660.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024111-46164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024111-13078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024111-90204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024109-77061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024109-82690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024111-36561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024111-60540.png)
由 ①②可知,
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024112-93782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024112-90653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024112-53885.png)
(3)取
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024113-54927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024113-20033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024113-89361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024113-95967.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024114-16082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024114-45437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024114-84346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024107-28078.png)
的平面角 11分
由(2)知
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024114-10672.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024115-21189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024115-10315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024107-28078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024108-65374.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024115-71817.png)
解法二 (1)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024115-39268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024109-82690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024111-36561.png)
建系
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024116-65689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024116-87948.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024116-32379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024117-25941.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024117-25608.png)
因为平面PAB的法向量
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024117-99440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024117-98631.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024118-18365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024118-27067.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024118-20115.png)
(3) 设平面PAD的法向量为
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024118-51100.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024119-63232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024119-23194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024119-41304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024119-89793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024119-73734.png)
平面PAB的法向量
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024117-99440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024120-35087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024107-28078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024108-65374.png)
核心考点
举一反三
A.m∥α,n∥α | B.m⊥α,n⊥α |
C.m∥α,n⊂α | D.m、n与α所成的角相等 |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024049-30480.png)
(1)求证:B1D1∥平面A1BD;
(2)求证:MD⊥AC;
(3)试确定点M的位置,使得平面DMC1⊥平面CC1D1D.
①
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024041-60100.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024041-59664.png)
③
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024041-14261.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024041-17324.png)
⑤
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024041-32462.png)
其中真命题的序号是__________________________(把所有真命题的序号都填上)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024031-37857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024031-86303.jpg)
(I)求证:BC∥平面EFG;
(II)求证:DH
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024031-37857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024012-86341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024012-86341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024012-20024.jpg)
(Ⅰ)求证:无论E点取在何处恒有
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024012-33684.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024013-61631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024012-86341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024013-83484.png)
(Ⅲ)在(Ⅱ)的条件下求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024013-14007.png)
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