题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010519-63939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010519-92922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010519-63763.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010520-80223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010520-48173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010520-13152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010520-40569.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010520-97512.jpg)
(1)证明:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010521-78560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010521-97857.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010521-64124.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010521-50450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010522-74333.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010522-16377.png)
解析
试题分析:解法1:(1)连结
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010522-43039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010522-30916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010520-13152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010520-40569.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010522-76258.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010522-34909.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010520-40569.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010523-61016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010523-79920.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010523-40723.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010522-74333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010521-50450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010522-74333.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010523-55278.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010521-97857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010522-74333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010524-18986.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010521-97857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010524-46857.jpg)
(2)在平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010522-74333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010524-72721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010524-29207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010524-98884.png)
由(1)知,平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010525-27504.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010522-74333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010525-66457.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010521-97857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010525-79023.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010525-93463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010521-97857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010526-30397.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010521-97857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010526-71946.png)
在平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010526-57227.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010524-72721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010526-10621.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010526-20119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010527-60379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010527-41191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010527-17632.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010527-38940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010527-39048.png)
从而
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010528-71757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010528-79390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010521-64124.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010528-13381.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010528-78134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010529-22429.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010529-34298.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010529-54392.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010529-47338.png)
故二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010521-64124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010522-16377.png)
解法2:如图所示,以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010524-72721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010529-85314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010530-34313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010530-78062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010530-40592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010530-43300.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010531-24919.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010531-13314.png)
(1)设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010531-62507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010522-74333.png)
则由
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010531-23804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010531-30818.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010532-28965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010532-92827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010532-24281.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010532-49362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010521-97857.png)
则由
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010532-64774.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010533-71509.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010533-49984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010533-74893.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010533-31888.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010533-81175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010534-82525.png)
从而平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010521-78560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010521-97857.png)
(2)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010530-78062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010524-18986.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010534-60828.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010534-60828.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010534-20224.png)
由(1)知,平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010521-97857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010533-31888.png)
设向量
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010534-54282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010535-40219.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010535-23606.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010535-32417.png)
所以二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010521-64124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010522-16377.png)
点评:主要是考查了面面垂直的判定定理以及二面角的平面角的求解,属于基础题。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010511-44512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010511-84933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010511-49369.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010511-80827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010511-95754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010511-49369.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010512-51058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010512-80465.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010502-95637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010502-41970.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010502-95637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010502-54058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010502-58354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010503-57582.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010503-22425.jpg)
(1)求证
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010503-64053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010503-86573.png)
(2)求证平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010503-65647.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010503-82519.png)
(3)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010504-55172.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010502-95637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010446-26026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010446-26026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010446-26026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010446-26026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010446-26026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010446-26026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010446-26026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010446-26026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010446-26026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010446-26026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010446-26026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010446-26026.png)
(1)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010446-26026.png)
(2)求平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010446-26026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010446-26026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010446-99178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010425-84171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010426-22072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010426-18455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010426-22167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010426-15971.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010427-35675.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010427-29141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010427-45293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010427-72134.png)
(Ⅰ)确定
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010427-29141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010427-67206.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010427-67206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010428-43920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010416-61768.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010416-12702.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010416-30352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010416-56098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010416-72973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010416-61463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010417-23224.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010417-31188.png)
(1)证明:无论
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010416-56098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010417-42760.png)
(2)当三棱柱
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010417-89692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010417-21541.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010418-13919.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010418-40700.png)
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