题目
题型:不详难度:来源:
(本小题满分14分)
在三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014526-12129.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014526-14155.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014526-44911.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014527-86217.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014527-49701.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014527-98457.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014527-99681.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014528-48196.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014528-51243.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014528-40531.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014528-22290.gif)
(1)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014529-29570.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014528-22290.gif)
(2)求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014529-54500.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014529-42826.gif)
答案
(1)略
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014529-75292.gif)
解析
证明:(1)如图,取
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014529-29570.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014530-91858.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014530-79949.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014530-43680.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014530-80732.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014530-27039.gif)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014526-14155.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014531-68613.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014531-28711.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014529-29570.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014531-61235.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014531-25275.gif)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014532-45908.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014531-61235.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014529-29570.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014528-22290.gif)
解:(2)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014528-48196.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014528-40531.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014532-71652.gif)
∵平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014527-49701.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014527-98457.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014530-27039.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014532-92379.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014527-98457.gif)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014532-67140.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014532-18265.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014533-61498.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014533-28036.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014527-98457.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014528-51243.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014528-22290.gif)
∴点
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014528-51243.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014527-98457.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014533-20394.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014533-65653.gif)
核心考点
试题【(本小题满分14分)在三棱锥中,是边长为的正三角形,平面⊥平面,,、分别为、的中点。(1)证明:⊥;(2)求三棱锥的体积.】;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6,正方形
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014517-68046.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014517-73179.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014518-64417.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014518-64417.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014517-73179.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014518-93057.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014517-73179.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014518-89676.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014517-73179.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014518-17257.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014518-47457.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014519-94346.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014517-73179.gif)
(1)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014519-61690.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014519-72249.gif)
(2)求三棱锥D-ABE的体积.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014519-59491.jpg)
如图,在等腰直角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014507-79173.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014507-21666.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014507-61758.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014507-38082.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014507-69752.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014507-62058.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014507-79173.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014507-50831.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014508-94550.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014508-97403.gif)
(1)对折后,在线段
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014508-95015.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014508-98841.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014508-82782.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014508-51452.gif)
(2)对折后,求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014508-85743.gif)
|
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014508-12558.gif)
已知直角梯形
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014441-33536.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014441-51132.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014441-24325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014442-49762.gif)
将
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014442-44576.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014442-31774.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014442-39923.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014442-81698.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014443-38808.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014443-82392.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014443-67837.gif)
(1)求异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014443-23281.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014443-52836.gif)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014444-81784.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014444-15711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014444-72453.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014444-83641.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014445-18093.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014445-92077.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014445-24475.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014445-18093.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014423-79113.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014423-98713.gif)
垂直于平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014424-34817.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014424-59975.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014424-71573.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014424-35629.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014424-39320.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014425-53020.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014425-54350.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014425-28572.gif)
(2)求平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014425-10509.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014424-34817.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014426-79530.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014418-19391.gif)
E为AB的中点
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014418-68347.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014419-53772.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014419-10104.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014419-85032.gif)
(2) 若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014418-68347.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014419-53772.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014419-18663.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014420-69194.gif)
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