题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031909-33970.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031909-19033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031909-82443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031909-89170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031909-73477.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031910-88967.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031910-72093.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031910-10271.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031910-42841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031910-21357.png)
(2)过
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031911-89681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031911-42775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031911-19914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031911-77092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031912-54622.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031912-45114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031912-97967.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031912-23505.png)
解析
试题分析:(1)问题需要证明的是线面平行,可以考虑通过证明线线平行来证明面面平行,而题中出现了中点,因此可以考虑通过构造三角形中位线来产生平行线:取
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031913-27767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031913-58462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031913-34039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031913-33535.png)
易证四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031913-49448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031910-42841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031913-33535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031914-11437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031910-21357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031914-32511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031910-21357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031911-77092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031912-54622.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031912-54622.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031914-61853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031911-89681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031914-34781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031915-29116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031915-24533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031911-77092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031915-13365.png)
不妨设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031915-82127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031915-48503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031916-22399.png)
试题解析:(1)如图,取
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031913-27767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031913-58462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031913-34039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031913-33535.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031916-64570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031909-19033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031913-34039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031916-37673.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031913-34039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031916-85876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031917-53537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031909-89170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031917-99767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031917-86147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031916-37673.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031917-86147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031916-85876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031913-34039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031917-99767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031913-34039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031917-86379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031913-49448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031910-42841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031913-33535.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031914-11437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031910-21357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031914-32511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031910-21357.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031910-42841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031910-21357.png)
连结
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031914-61853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031911-89681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031914-34781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031915-29116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031909-19033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031909-82443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031909-89170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031909-19033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031909-82443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031911-89681.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031911-89681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031909-82443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031909-19033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031911-89681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031909-82443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031914-61853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031917-21124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031911-89681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031909-82443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031918-75829.png)
从而
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031918-29154.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031918-31038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031915-24533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031911-77092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031915-13365.png)
不妨设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031915-82127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031909-73477.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031910-88967.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031918-52922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031918-73777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031919-66153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031919-50890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031919-87282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031919-83920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031920-99352.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031916-22399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031920-21321.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031859-32125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031859-95629.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031855-14705.jpg)
A.AC⊥SB |
B.AB∥平面SCD |
C.SA与平面SBD所成的角等于SC与平面SBD所成的角 |
D.AB与SC所成的角等于DC与SA所成的角 |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031848-68307.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031839-50779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031840-69436.jpg)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022031828-18325.png)
①AF⊥PB; ②EF⊥PB;
③AF⊥BC; ④AE⊥平面PBC.
其中正确命题的序号是 .
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