题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124827-32325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124827-71049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124827-81607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124827-75750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124828-87142.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124828-86168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124828-23337.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124828-21083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124829-16203.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124828-86168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124829-39078.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124828-23337.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124828-21083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124829-47727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124829-68384.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124829-59631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124830-18665.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124830-14117.png)
解析
试题分析:(1)由线面垂直判定定理,要证线面垂直,需证
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124828-86168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124829-39078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124827-81607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124828-87142.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124828-86168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124828-86168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124830-49950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124827-71049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124827-75750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124830-81163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124828-86168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124830-81767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124829-47727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124829-68384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124828-23337.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124828-21083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124830-18665.png)
试题解析:证明:(1)因为E是AD的中点,PA=PD,所以AD⊥PE.
因为底面ABCD是菱形,∠BAD=
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124830-40534.png)
因为PE∩BE=E,所以AD⊥平面PBE. 4分
(2)连接AC交BD于点O,连结OQ.因为O是AC中点,
Q是PC的中点,所以OQ为△PAC中位线.所以OQ//PA. 7分
因为PA
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124831-82869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124831-91576.png)
(3)设四棱锥P-BCDE,Q-ABCD的高分别为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124831-83409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124831-75187.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124831-60662.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124831-83409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124831-60662.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124831-75187.png)
因为VP-BCDE=2VQ-ABCD,且底面积SBCDE=
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124832-82826.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124832-38664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124832-19578.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124830-14117.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124819-69601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124819-52447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124820-78909.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124808-33436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124808-72426.jpg)
⑴试用半径
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124809-18696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124809-31129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124809-18696.png)
⑵当圆柱高
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124810-26744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124809-18696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124809-31129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124755-11172.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124741-87180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124741-71108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124742-76884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124741-71108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124742-80984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124742-79670.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124742-83546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124743-95885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124743-27373.jpg)
(1)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124743-17811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124743-66361.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124743-50573.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021124744-65003.png)
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