题目
题型:不详难度:来源:
A.m∥α,n∥β且α∥β,则m∥n |
B.m⊥α,n⊥β且α⊥β,则m⊥n |
C.m⊥α,n⊂β,m⊥n,则α⊥β |
D.m⊂α,n⊂α,m∥β,n∥β,则α∥β |
答案
解析
对于B,由m⊥α,n⊥β且α⊥β,则m与n一定不平行,否则有α∥β,与已知α⊥β矛盾,通过平移使得m与n相交,
且设m与n确定的平面为γ,则γ与α和β的交线所成的角即为α与β所成的角,因为α⊥β,所以m与n所成的角为90°,
故命题B正确.
对于C,根据面面垂直的性质,可知m⊥α,n⊂β,m⊥n,∴n∥α,∴α∥β也可能α∩β=l,也可能α⊥β,故C不正确;
对于D,若“m⊂α,n⊂α,m∥β,n∥β”,则“α∥β”也可能α∩β=l,所以D不成立.
故选B.
核心考点
试题【设m,n是两条不同直线,α,β是两个不同的平面,下列命题正确的是( )A.m∥α,n∥β且α∥β,则m∥nB.m⊥α,n⊥β且α⊥β,则m⊥nC.m⊥α,n⊂】;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/20191106/20191106014848-88690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014848-74877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014848-82100.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014848-74877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014848-90490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014848-51614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014848-13460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014848-12074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014849-35239.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014849-27421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014849-27422.png)
(Ⅱ)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014849-11043.png)
(Ⅲ)在棱
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014849-40827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014849-75183.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014849-96256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014850-41785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014849-75183.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014850-11910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014838-88196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014838-96718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014838-61585.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014838-96718.png)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014838-91212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014838-98344.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014839-48339.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014839-36828.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014839-67804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014839-58835.png)
(Ⅱ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014839-93435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014840-85882.png)
(Ⅲ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014840-81564.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014840-41351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014840-10045.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014840-81877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014827-57380.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014827-14313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014828-27749.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014828-74879.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014828-96462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014828-76576.jpg)
(1)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014829-37999.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014829-15842.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014829-59513.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014829-58699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014830-41629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014829-15842.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014830-95118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014830-22711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014830-89939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014814-20790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014814-52859.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014814-59851.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014814-49863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014814-91184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014814-32783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014814-67168.png)
(1)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014814-10104.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014815-38095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014752-34188.png)
如图,在三棱柱
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014752-40897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014752-26328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014753-20570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014753-42572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014753-26205.png)
(1)求证:AB⊥平面AA1 C1C;
(2)若线段
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014753-25441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014753-96918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014753-87033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014753-14478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014753-96918.png)
(3)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014754-14527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106014754-16118.png)
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