题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050126-49484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050127-63479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050127-35185.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050127-38136.jpg)
⑴ 求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050127-36903.png)
⑵ 求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050127-78766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050127-81210.png)
⑶ 求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050128-14823.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050128-69987.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050128-68863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050128-46966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050129-89320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050129-82750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050127-36903.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050129-96706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050129-83709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050129-31032.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050130-60835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050129-96706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050127-63479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050130-29218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050130-69930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050127-78766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050127-81210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050130-89687.png)
解析
试题分析:(1)连接BD,AE. 因四边形ABCD为正方形,故
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050128-69987.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050130-11082.jpg)
因
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050128-68863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050131-19492.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050128-46966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050131-10959.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050129-89320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050129-82750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050131-72988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050129-82750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050127-36903.png)
⑵. 连接
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050129-96706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050129-83709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050129-31032.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050130-60835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050129-96706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050127-63479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050130-29218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050129-31032.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050131-81511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050130-69930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050132-27561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050127-81210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050132-88532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050127-81210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050127-78766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050127-81210.png)
⑶. 由⑵知,点A到平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050127-81210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050127-81210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050128-14823.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050132-78837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050132-75041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050128-14823.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050130-89687.png)
点评:要证明线面平行常借助于平面外一直线与平面内一直线平行;线面的垂直关系中常用的思路是线线垂直与线面垂直的互相转化;第三问求三棱锥体积时采用等体积法的思路转化底面和顶点,是底面积和高都容易求出
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050113-46946.jpg)
(1)求正三棱台ABC-A1B1C1的体积;
(2)求平面EA1B1与平面A1B1C1的夹角的余弦;
(3)若P是棱A1C1上一点,求CP+PB1的最小值.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050100-25828.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050100-42755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050100-90370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050101-25118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050101-40520.jpg)
(Ⅰ) 求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050101-38806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050101-41351.png)
(Ⅱ) 求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050101-13056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050101-41351.png)
(Ⅲ) 求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050101-95247.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050050-37290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050050-85242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050051-34913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050051-95364.png)
(Ⅰ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050051-71890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050051-60514.png)
(Ⅱ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050052-38078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050037-96031.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050037-15173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050037-25890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050037-44695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050038-78252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050038-52982.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050038-63532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050038-56473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050039-84685.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050039-56039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050038-63532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050038-56473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050039-84685.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050039-97969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050022-12478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050022-56939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050023-93784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050023-37494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050023-28960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050023-26092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050023-43026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050024-57077.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050024-26987.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050024-27536.png)
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