题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032250-26855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-13773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-27481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-13773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-26810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-13773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-74416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-60118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-75980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-97377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-61287.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-42472.png)
(Ⅱ)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-10417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-15627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032253-24425.jpg)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-10417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-15627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032253-29941.png)
解析
(1)第一问中要证明面面垂直关键是证明线面垂直,然后利用判定定理得到。
(2)第二问先根据线面角的定义,作出线面角,然后利用直角三角形的边角的关系求解的得到。
解:(1)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-26810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-13773.png)
是
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-74416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-60118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-75980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032253-13591.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-27481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-13773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-13773.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032253-18313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032253-20281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032254-77895.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032254-59417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032254-20965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032254-67006.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-42472.png)
(2)解法一:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-27481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-13773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032254-40639.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032254-61214.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032255-83790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-15627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032255-86889.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032255-14849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032255-22098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032255-26401.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032256-33132.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032256-77080.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032256-14787.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032256-49987.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032257-80854.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-10417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-15627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032257-32269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032257-66798.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032257-55271.png)
∴直线
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-10417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-15627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032253-29941.png)
解法二:分别以
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032257-82387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032258-42779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032258-52648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032258-43675.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032258-75252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032259-53066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032259-49303.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032259-89677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032259-73008.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032300-52894.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032300-97991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032300-83289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032300-30790.png)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032301-57408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-15627.png)
∴平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-15627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032301-94255.png)
设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-10417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-15627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032301-87796.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032301-88047.png)
∴直线
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-10417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-15627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032253-29941.png)
解:(1)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-26810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-13773.png)
是
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-74416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-60118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-75980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032253-13591.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-27481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-13773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-13773.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032253-18313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032253-20281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032254-77895.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032254-59417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032254-20965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032254-67006.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-42472.png)
(2)解法一:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-27481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032251-13773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032254-40639.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032254-61214.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032255-83790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-15627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032255-86889.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032255-14849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032255-22098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032255-26401.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032256-33132.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032256-77080.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032256-14787.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032256-49987.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032257-80854.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-10417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-15627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032257-32269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032257-66798.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032257-55271.png)
∴直线
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-10417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-15627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032253-29941.png)
解法二:分别以
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032257-82387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032258-42779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032258-52648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032258-43675.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032258-75252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032259-53066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032259-49303.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032259-89677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032259-73008.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032300-52894.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032300-97991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032300-83289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032300-30790.png)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032301-57408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-15627.png)
∴平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-15627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032301-94255.png)
设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-10417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-15627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032301-87796.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032301-88047.png)
∴直线
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-10417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032252-15627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032253-29941.png)
核心考点
试题【(本题满分15分)如图,在四棱锥中,底面是矩形,平面,与平面所成角的正切值依次是和,,依次是的中点.(Ⅰ)求证:;(Ⅱ)求直线与平面所成角的正弦值.】;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/20191106/20191106032237-44366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032237-65123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032237-23514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032237-66849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032238-23062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032238-65754.png)
(Ⅰ)平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032238-80807.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032239-95698.png)
(Ⅱ)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032239-48194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032237-65123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032229-61555.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032229-37940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032229-17970.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032229-25741.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032229-37940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032229-25741.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() ![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032224-31951.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032225-37609.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032225-23682.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032225-22241.jpg)
(1)求证:EF∥平面CB1D1;
(2)求证:平面CAA1C1⊥平面CB1D1
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032217-78916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032211-97508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032211-97539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032211-74611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032211-64833.png)
A.若![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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