题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071659-72880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071659-40314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071659-87363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071659-80254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071700-94589.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071700-64833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071700-86105.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071700-93365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071701-37128.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071659-80254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071701-45286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071701-50814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071701-37128.png)
(Ⅲ)是否存在点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071700-94589.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071701-20748.png)
由.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071702-15320.jpg)
答案
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071702-97430.png)
∴BC⊥平面PAC. ………3分
(Ⅱ)∵D为PB的中点,DE//BC,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071702-38739.png)
又由(Ⅰ)知,BC⊥平面PAC,
∴DE⊥平面PAC,垂足为点E.
∴∠DAE是AD与平面PAC所成的角,
∵PA⊥底面ABC,∴PA⊥AB,又PA=AB,
∴△ABP为等腰直角三角形,∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071703-83471.png)
∴在Rt△ABC中,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071703-71298.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071703-66342.png)
∴在Rt△ADE中,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071703-70253.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071704-25339.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071704-32570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071704-94290.png)
(Ⅲ)∵AE//BC,又由(Ⅰ)知,BC⊥平面PAC,∴DE⊥平面PAC,
又∵AE
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071704-68851.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071704-68851.png)
∴∠AEP为二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071705-70281.png)
∵PA⊥底面ABC,∴PA⊥AC,∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071705-55682.png)
∴在棱PC上存在一点E,使得AE⊥PC,这时
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071705-55610.png)
故存在点E使得二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071705-70281.png)
【解法2】如图,以A为原煤点建立空间直角坐标系
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071706-82209.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071706-36552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071706-25403.png)
(Ⅰ)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071707-66798.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071707-20848.png)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071702-97430.png)
(Ⅱ)∵D为PB的中点,DE//BC,∴E为PC的中点,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071707-88284.png)
∴又由(Ⅰ)知,BC⊥平面PAC,∴∴DE⊥平面PAC,垂足为点E.
∴∠DAE是AD与平面PAC所成的角,
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071707-97113.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071707-98212.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071704-25339.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071704-32570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071708-68539.png)
(Ⅲ)同解法1.
解析
核心考点
试题【. (本小题满分10分)如图,在三棱锥中,底面,点,分别在棱上,且(Ⅰ)求证:平面;(Ⅱ)当为的中点时,求与平面所成的角的大小;(Ⅲ)是否存在点使得二面角为直二】;主要考察你对线线角等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071644-54202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071644-83810.png)
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071644-88225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071645-64158.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071645-67170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071645-97668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071645-67170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071645-43379.png)
其中正确的命题有( )
A.1个 | B.2个 | C.3个 | D.4个 |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071640-45326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071640-57138.png)
(1)证明:CM⊥SN;
(2)求SN与平面CMN所成角的大小;
(3)求三棱锥P-ABC外接球的体积V。
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071641-51226.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071631-49588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071631-38205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071631-50921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071631-80631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071632-63665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071632-50373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071632-56392.png)
⑴求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071632-85680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071633-52195.png)
⑵当
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071633-23172.png)
如图,在直三棱柱
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071622-62827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071622-27989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071623-29228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071623-40046.png)
(1)求三棱柱
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071622-62827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071623-57203.png)
(2)求异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071623-44531.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071623-92519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071624-72781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071611-35786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071611-38548.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071611-20847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071611-44910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071611-89194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071611-70665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071611-58880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071611-56481.png)
(Ⅰ)证明:面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071611-33841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071612-81502.png)
(Ⅱ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071612-53184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071611-56481.png)
(Ⅲ)求面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071612-70429.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071612-81844.png)
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