题目
题型:不详难度:来源:
在长方体
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012720-61909.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012720-31780.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012720-12941.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012720-32072.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012720-49619.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012720-29473.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012721-74643.jpg)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012720-12941.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012721-29724.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012721-20762.gif)
(2)在(Ⅰ)成立的条件下,求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012721-56973.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012720-12941.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012720-32072.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012721-29724.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012721-24957.gif)
证明:取
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012721-87933.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012721-29724.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012721-47831.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012721-19599.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012721-19599.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012722-37180.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012722-29463.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012722-84692.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012722-56449.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012722-37180.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012721-29724.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012722-56449.gif)
方法二)延长
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012722-53141.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012722-18840.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012722-88412.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012722-39158.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012722-21734.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012722-78503.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012723-92978.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012720-49619.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012720-29473.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012722-37180.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012721-29724.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012722-39158.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012722-29463.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012722-39158.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012723-61773.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012722-56449.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012722-37180.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012721-29724.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012722-56449.gif)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012720-12941.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012720-32072.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012723-78444.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012723-12685.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012723-26780.gif)
可知
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012723-51173.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012723-82634.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012723-78690.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012724-72954.gif)
所以二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012724-85575.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012724-10762.gif)
又二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012724-22573.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012724-15048.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012724-85575.gif)
只需求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012724-15048.gif)
过A点作
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012724-75405.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012724-42298.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012724-25811.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012725-32379.gif)
过F作
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012725-57256.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012725-13745.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012724-15048.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012725-70210.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012725-66856.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012725-40925.gif)
所以二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012724-22573.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012726-89674.gif)
解析
核心考点
试题【(本小题满分12分)在长方体中,点是上的动点,点为的中点. (1)当点在何处时,直线//平面,并证明你的结论;(2)在(Ⅰ)成立的条件下,求二面角的大小.】;主要考察你对空间几何体的结构特征等知识点的理解。[详细]
举一反三
如图5,在三棱柱
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012657-64756.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012657-48746.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012658-27697.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012658-92219.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012658-97008.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012658-12591.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012658-36393.gif)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012659-54080.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012659-93964.gif)
(2) 求四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012659-29512.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012659-16916.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012651-18353.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012651-24122.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012651-59777.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012651-42625.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012652-68499.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012652-60267.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012652-74004.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012652-19411.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012641-12865.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012641-70093.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012641-42685.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012641-41895.gif)
已知
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012641-97845.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012642-21465.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012641-42685.gif)
图形(
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012642-71931.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012642-83313.gif)
①动点
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012642-71931.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012642-52736.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012641-70093.gif)
②平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012643-11011.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012643-36943.gif)
③三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012643-75763.gif)
④异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012643-82464.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012643-55214.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012644-26866.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012626-99529.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012626-74128.png)
(1)求证:AC⊥BC1;
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012626-22477.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012620-95242.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012620-27114.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021012620-80912.gif)
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