题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024311-67376.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024311-44820.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024311-37098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024311-16990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024312-52937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024312-67022.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024312-23938.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024312-85628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024313-58451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024313-23253.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024313-65914.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024313-73601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024314-91583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024314-85577.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024314-85577.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024314-98478.png)
解析
试题分析:(1)证明线面平行,有两种思路,一是证线面平行,二通过面面平行来证明.在本题中,两种思路比较,可以看出,取AC的中点P,证明平面MPN∥平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024314-91583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024314-65985.png)
(2)首先作出二面角的平面角. 由于平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024311-37098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024311-16990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024315-12841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024315-55794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024315-88345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024315-17361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024316-74761.png)
从而
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024315-17361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024311-16990.png)
再过点B作BO⊥CN于O、连
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024316-68774.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024316-53615.png)
所以∠
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024316-20503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024314-85577.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024317-42556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024316-20503.png)
试题解析:(1)取AC的中点P,连MP、NP。易证MP∥
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024317-31078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024314-91583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024314-91583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024314-65985.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024317-43764.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024315-12841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024315-55794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024315-88345.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024315-17361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024316-74761.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024315-17361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024311-16990.png)
过点B作BO⊥CN于O、连
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024316-68774.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024316-53615.png)
所以∠
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024316-20503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024314-85577.png)
又易求
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024317-50887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024318-33327.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024318-94446.png)
也即二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024314-85577.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024314-98478.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024255-15805.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024255-88023.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024255-32068.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024255-88023.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024255-25817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024256-94503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024256-51996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024256-35815.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024256-78084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024257-48093.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024257-45261.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024257-17297.png)
(Ⅰ)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024257-32118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024258-16334.png)
(Ⅱ)设二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024258-61395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024258-68426.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024258-87397.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024259-24406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024259-10828.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024259-54132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024249-98122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024249-51205.png)
①若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024249-98122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024249-42330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024249-98122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024250-14982.png)
②若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024249-98122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024249-51205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024250-68578.png)
③设
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024250-30714.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024249-98122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024249-42330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024250-64834.png)
④若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024251-79083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024249-98122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024251-76733.png)
上面的命题中,真命题的序号是 ( )
A.①③ | B.②④ | C.①② | D.③④ |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024237-58291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024237-81452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024237-29164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024237-34492.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024238-70447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024238-77717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024238-35263.png)
(1)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024238-83276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024239-76024.png)
(2)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024239-53168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024239-76024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024239-53041.png)
求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024240-72723.png)
A.若m⊥n,则α⊥β | B.若α⊥β,则m⊥n |
C.若m∥n,则α∥β | D.若α∥β,则m∥n |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024222-53949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024223-92445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024223-26652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024223-64218.png)
①
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024223-92445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024223-64218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024223-98669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024222-53949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024223-92445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024223-64218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024223-98669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024222-53949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024222-53949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024223-98669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024223-92445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024223-64218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024222-53949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024223-98669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024223-92445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106024223-64218.png)
其中正确命题序号是 .
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