题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082932-21988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-14204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-31441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-31441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-14204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-96683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-14204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-78162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-14204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-20671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-94258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-20587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-14204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-83354.jpg)
(1)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-69273.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-52643.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-83497.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-83497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-47679.png)
解析
(1)要证明面面垂直,只要证明线面垂直,再结合面面垂直的判定定理得到结论。
(2)合理的建立空间直角坐标系,然后求解得到平面的法向量和法向量,运用向量的夹角公式得到二面角的平面角的求解。
(1)证明:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-96683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-14204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-31441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-14204.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-41007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-31441.png)
在正方形
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-88328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-50981.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-79505.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-81811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-52643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-47528.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-88328.png)
∴平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-69273.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-52643.png)
(2)解法1:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-26735.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-81811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-52643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-77428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-52643.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-25505.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-55515.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-14204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-86729.png)
设正方形
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-88328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-20709.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-86532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-43057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-21729.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-86532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-52643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-65951.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-90716.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-50302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082936-77940.png)
过点
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-78162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082936-94920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082936-71744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082936-74623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082936-73083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082936-82416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082936-68882.png)
由于
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082937-83670.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-52643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082937-65770.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-52643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082937-38155.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082937-36314.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082937-49268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-88328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082937-75835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-88328.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082937-67321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082937-37596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082937-26816.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082937-46826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082937-19407.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082938-64344.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082937-19407.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082938-63562.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082938-86835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-83497.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-86532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-52643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082938-79849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-20587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082938-19077.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082938-73564.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082938-90559.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-86532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082937-19407.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082938-95610.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082938-16622.png)
故二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-83497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-47679.png)
解法2:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-81811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-52643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-77428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-52643.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-25505.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-55515.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-14204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-86729.png)
设正方形
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-88328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-20709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-86532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-43057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-21729.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-86532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-52643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-65951.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-90716.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082935-50302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082936-77940.png)
以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-94258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082938-12289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082933-31441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082938-61561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082939-97338.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082939-52591.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082939-39502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082939-92258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082939-24336.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082939-14126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082939-65342.png)
设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-88328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082939-96752.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082939-73008.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082940-49012.png)
取
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082940-62523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082940-11164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-88328.png)
设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082940-75327.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082940-11791.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082941-76999.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082941-42648.png)
取
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082941-39387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082941-93816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-88328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082941-79475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082942-48795.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082942-58160.png)
故二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-83497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082934-47679.png)
核心考点
试题【如图,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切】;主要考察你对空间几何体的视图与直观图等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082920-40382.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082915-12689.png)
(1)若∠ADE=,求证:CE⊥平面PDE;
(2)当点A到平面PDE的距离为时,求三棱锥A-PDE的侧面积.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082910-99512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082910-35189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082910-36678.png)
(1)求证:四点
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082911-32464.png)
(2)平面ABCD
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082911-24556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082905-25088.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082905-60308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082905-13866.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082905-14806.jpg)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082906-70097.png)
(2)求平面PAD与平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082906-36762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082906-95194.png)
(3)求
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021082906-23278.png)
A.内心 | B.重心 | C.外心 | D.垂心 |
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