题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-55587.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-44229.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-96189.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-96189.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-44229.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-56112.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-44229.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-97525.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-44229.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-72367.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-44506.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-41863.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-44229.gif)
(1)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-94963.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-22383.gif)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-49377.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-39177.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-24551.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-56112.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-44229.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-96189.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-44229.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-97522.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-96189.gif)
在正方形
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-55587.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-21986.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-83689.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-12443.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-22383.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-88753.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-55587.gif)
∴平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-94963.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-22383.gif)
(2)解法1:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-12443.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-22383.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-35502.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-22383.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-25748.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-37702.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-44229.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-69370.gif)
设正方形
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-55587.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-33368.gif)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-93325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035712-11664.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035712-38762.gif)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-93325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-22383.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035712-40789.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035712-83911.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035712-88901.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035712-96884.gif)
过点
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-97525.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035712-56213.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035712-44489.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035712-41114.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035713-52403.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035713-90601.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035713-38639.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035713-24770.gif)
由于
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035713-35107.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-22383.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035713-70503.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-22383.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035713-19733.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035713-47490.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035714-19881.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-55587.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035714-48911.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-55587.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035714-62042.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035714-17403.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035714-60897.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035714-45732.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035714-19847.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035714-49650.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035714-19847.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035715-71234.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035715-35595.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-49377.gif)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-93325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-22383.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035715-77353.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-41863.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035715-40605.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035715-58964.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035716-70679.gif)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-93325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035714-19847.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035716-42269.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035716-87726.gif)
故二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-49377.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-24551.gif)
解法2:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-12443.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-22383.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-35502.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-22383.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-25748.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-37702.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-44229.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-69370.gif)
设正方形
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-55587.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-33368.gif)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-93325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035712-11664.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035712-38762.gif)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035711-93325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-22383.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035712-40789.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035712-83911.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035712-88901.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035712-96884.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035716-11468.gif)
以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-44506.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035716-26181.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-96189.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035717-76628.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035717-98353.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035717-72394.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035717-21117.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035717-39468.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035718-24798.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035718-11719.gif)
设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-55587.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035718-68107.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035718-39568.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035718-36826.gif)
取
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035719-38611.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035719-49302.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-55587.gif)
设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035719-74317.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035719-48492.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035720-88213.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035720-36360.gif)
取
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035720-55895.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035720-49111.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035709-55587.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035720-72092.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035721-65743.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035721-88762.gif)
故二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-49377.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035710-24551.gif)
核心考点
试题【如图6,正方形所在平面与圆所在平面相交于,线段为圆的弦,垂直于圆所在平面,垂足是圆上异于、的点,,圆的直径为9.(1)求证:平面平面;(2)求二面角的平面角的正】;主要考察你对空间几何体的结构特征等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035655-80171.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035655-18168.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035655-91118.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035656-75796.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035656-92762.gif)
求证:(1)直线
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035656-61987.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035656-84399.gif)
(2)平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035656-41347.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035657-92854.gif)
(1)求证: BD⊥平面ACC1
(2)求二面角C1—BD—C的正切值
![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035641-46468.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035642-63856.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035642-92736.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035642-36791.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035642-49666.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035643-48035.gif)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035643-59983.gif)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035643-64198.gif)
(3)求
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035643-79211.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035643-78112.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035630-40160.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035630-56918.gif)
①求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035630-43871.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035630-31213.gif)
②求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035631-59025.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035630-31213.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035631-73555.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035631-78918.gif)
![]() |
(1)若CG=AC,求异面直线PG与CD所成角的大小;
(2)若CG=AC,求点C到平面PBG的距离;
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035607-18582.jpg)
(3)当点G在AC的延长线上运动时(不含端点C),求二面角P-BG-C的取值范围。
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