题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034226-17264.jpg)
(1).求证:EA⊥EC;
(2).设平面ECD与半圆弧的另一个交点为F。
①求证:EF//AB;
②若EF=1,求三棱锥E—ADF的体积
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034226-44172.png)
解析
试题分析:本题主要考查线面的位置关系、几何体的体积等基础知识,意在考查考生的空间想象能力推理论证能力.第一问,由AB为圆的直径,得
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034226-91681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034226-86542.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034226-49328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034227-59083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034227-98748.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034227-91384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034227-25775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034226-49328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034227-25775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034227-57423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034227-57423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034228-43815.png)
试题解析:(1)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034228-97609.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034228-94260.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034228-28071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034226-91681.png)
又∵平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034229-86187.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034229-62288.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034226-49328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034229-75174.png)
由面面垂直性质定理得
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034226-86542.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034226-49328.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034229-46061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034226-49328.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034227-59083.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034230-62949.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034227-98748.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034227-91384.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034230-97640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034227-91384.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034230-26031.png)
(2)①由
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034227-25775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034228-43815.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034227-25775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034226-49328.png)
又∵平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034230-77934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034230-35072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034230-63684.png)
∴根据线面平行的性质定理得
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034227-25775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034227-57423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034227-25775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034228-43815.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034227-57423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034228-43815.png)
②
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034231-39105.png)
核心考点
试题【如图,E是以AB为直径的半圆弧上异于A,B的点,矩形ABCD所在平面垂直于该半圆所在的平面,且AB=2AD=2。(1).求证:EA⊥EC;(2).设平面ECD与】;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/20191022/20191022034222-45574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034222-97057.png)
⑴求证:平面PAD⊥面PBD;
⑵当Q在什么位置时,PA∥平面QBD?
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034218-73831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034219-51474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034219-51474.png)
A.[0,![]() | B.[![]() | C.[![]() | D.[![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034205-71791.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034205-98922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034205-73021.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034205-98922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034205-90978.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034206-72699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034206-22780.png)
(1)问当PA的长为多少时,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034206-92308.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034206-68487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034148-54160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034148-59688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034149-76960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034149-54568.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034148-59688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034149-66756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034149-66499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034149-74222.png)
(1)问当PA的长为多少时,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034150-86410.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034150-41248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034143-52102.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034143-84395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034143-24382.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034143-48629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034143-10777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034143-84395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034143-50077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034143-61141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034144-57137.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034144-34867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034144-97662.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034144-67584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034144-34905.png)
(3)求
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034144-25050.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022034145-94082.png)
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