题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010545-17351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010545-25467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010545-58468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010545-56607.png)
(Ⅰ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010545-35474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010546-12533.png)
(Ⅱ)求二面角D-
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010546-55661.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010546-33735.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010546-99442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010546-55661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010546-99442.png)
OD∥
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010545-35474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010546-28380.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010546-12533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010545-35474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010547-92194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010546-12533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010545-35474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010546-12533.png)
(Ⅱ)由
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010545-25467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010545-58468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010547-33081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010545-25467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010547-17126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010547-59832.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010547-79543.jpg)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010548-92804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010548-20856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010548-65513.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010548-93470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010548-57510.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010548-21782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010549-40301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010549-32470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010546-12533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010549-14451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010549-46822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010549-95695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010550-47682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010550-27282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010546-12533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010550-41199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010550-32254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010550-77340.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010551-48551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010551-47721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010551-35809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010546-55661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022010546-33735.png)
本题第(Ⅰ)问,证明直线与平面平行,主要应用线面平行的判定定理,一般情况下,遇到中点想中位线的思想要用上,同时用上侧面为平行四边形的条件;第(Ⅱ)问,求二面角的大小,若图形中容易建立空间直角坐标系,则就求两个半平面的法向量,从需得出结果.对第(Ⅰ)问,证明线面平行时,容易漏掉条件;对第(Ⅱ)问,二面角的大小与两个法向量夹角相等或互补的关系,一部分同学容易得出它们相等.
【考点定位】本小题考查空间中直线与平面平行等位置关系的证明、二面角的求解,考查同学们的逻辑推理能力、空间想象能力,考查分析问题以及解决问题的能力.
核心考点
举一反三
![](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)
![](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)
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