解答题-证明题 适中0.64 引用2 组卷216
已知四面体
中,
,平面
平面
,
分别为棱
和
的中点.
![](https://img.xkw.com/dksih/QBM/2015/1/6/1571951138316288/1571951144083456/STEM/f5858262611849c39d51dbcae8bc947d.png)
(1)求证:
平面
;
(2)求证:
;
(3)若
内的点
满足
∥平面
,设点
构成集合
,试描述点集
的位置(不必说明理由)
![](https://img.xkw.com/dksih/QBM/2015/1/6/1571951138316288/1571951144083456/STEM/aa0a956b5de646dcb61c7cdef55e0a05.png)
![](https://img.xkw.com/dksih/QBM/2015/1/6/1571951138316288/1571951144083456/STEM/2fb5c8f37244465c9cc0c254c2f9d131.png)
![](https://img.xkw.com/dksih/QBM/2015/1/6/1571951138316288/1571951144083456/STEM/ed9b453916ca48dda353543da37562d6.png)
![](https://img.xkw.com/dksih/QBM/2015/1/6/1571951138316288/1571951144083456/STEM/5519e6f905e64b54aa52165c09662b61.png)
![](https://img.xkw.com/dksih/QBM/2015/1/6/1571951138316288/1571951144083456/STEM/f7b5bd1ec00948fcb635fc61203301cd.png)
![](https://img.xkw.com/dksih/QBM/2015/1/6/1571951138316288/1571951144083456/STEM/91a9350c3c0a447291e9f470d624e166.png)
![](https://img.xkw.com/dksih/QBM/2015/1/6/1571951138316288/1571951144083456/STEM/0cf8e1ac5b084388a86787a4696caaca.png)
![](https://img.xkw.com/dksih/QBM/2015/1/6/1571951138316288/1571951144083456/STEM/f5858262611849c39d51dbcae8bc947d.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2015/1/6/1571951138316288/1571951144083456/STEM/b9f3cca15773452e8b2f38285790bf5f.png)
![](https://img.xkw.com/dksih/QBM/2015/1/6/1571951138316288/1571951144083456/STEM/5519e6f905e64b54aa52165c09662b61.png)
(2)求证:
![](https://img.xkw.com/dksih/QBM/2015/1/6/1571951138316288/1571951144083456/STEM/7c529b587925474a81db0e3ad62e307d.png)
(3)若
![](https://img.xkw.com/dksih/QBM/2015/1/6/1571951138316288/1571951144083456/STEM/00deb7b0151c486da4a27a288e0e12f4.png)
![](https://img.xkw.com/dksih/QBM/2015/1/6/1571951138316288/1571951144083456/STEM/efc6abe1afea42d5826e960a0e18931a.png)
![](https://img.xkw.com/dksih/QBM/2015/1/6/1571951138316288/1571951144083456/STEM/e4ed4eb2090c461c8fdb7834f7f725a1.png)
![](https://img.xkw.com/dksih/QBM/2015/1/6/1571951138316288/1571951144083456/STEM/5519e6f905e64b54aa52165c09662b61.png)
![](https://img.xkw.com/dksih/QBM/2015/1/6/1571951138316288/1571951144083456/STEM/efc6abe1afea42d5826e960a0e18931a.png)
![](https://img.xkw.com/dksih/QBM/2015/1/6/1571951138316288/1571951144083456/STEM/22929a9bd04a4279af56290a47a6d830.png)
![](https://img.xkw.com/dksih/QBM/2015/1/6/1571951138316288/1571951144083456/STEM/22929a9bd04a4279af56290a47a6d830.png)
2011·江苏泰州·一模
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