题目
题型:不详难度:来源:
![](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.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050113-18800.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050113-74179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050114-85120.png)
解析
试题分析:(1)由题意
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050114-98426.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050114-63179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050114-41119.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050115-41348.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050115-62557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050115-74638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050115-54439.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050115-99793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050116-46675.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050116-46675.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050116-58732.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050116-44779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050116-46959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050117-74446.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050117-68511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050117-67868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050117-38674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050117-33773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050118-60588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050118-55001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050118-64908.png)
设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050118-49424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050119-65981.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050119-49315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050119-96169.png)
取
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050119-84955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050119-45958.png)
量
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050120-85939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050120-31901.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050113-74179.png)
(3)将梯形
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050120-54759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050120-60118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050121-17021.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050121-53185.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050121-23297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050121-48140.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050121-84534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050122-75855.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050122-22779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050114-85120.png)
点评:中档题,立体几何题,是高考必考内容,往往涉及垂直关系、平行关系、角、距离、体积的计算。在计算问题中,有“几何法”和“向量法”。利用几何法,要遵循“一作、二证、三计算”的步骤。利用向量则简化了证明过程,对计算能力要求高。
核心考点
试题【(理科)(本小题满分12分)如图分别是正三棱台ABC-A1B1C1的直观图和正视图,O,O1分别是上下底面的中心,E是BC中点.(1)求正三棱台ABC-A1B1】;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/20191022/20191022050100-25828.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)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050015-25760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050015-71053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050015-19986.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050015-41521.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050015-40547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050015-34839.png)
⑴求异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050015-21269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050015-86401.png)
⑵若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050016-38710.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050016-60892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050016-79781.png)
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