1 . 已知
表示一条直线,
,
表示两个不重合的平面,有以下三个语句:①
;②
;③
.以其中任意两个作为条件,另外一个作为结论,可以得到三个命题,其中正确命题的个数是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d1a34ae2b8c77f8d7e355c6d1d667e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74c62c14a017007a6bdfe25eada9c433.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f636ffb1c966151260fb82604d2916.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2465d2267f1ab09dcd30dc0a2f080348.png)
![](https://img.xkw.com/dksih/QBM/2014/2/28/1571536298901504/1571536304472064/STEM/ca2e4fb06b794271a9ad54d0c4733251.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 如图1,在直角梯形
中,
,
,
,
. 把
沿对角线
折起到
的位置,如图2所示,使得点
在平面
上的正投影
恰好落在线段
上,连接
,点
分别为线段
的中点.
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/8703f1c61cd041c8b5350497a90f0a1e.png)
(1)求证:平面
平面
;
(2)求直线
与平面
所成角的正弦值;
(3)在棱
上是否存在一点
,使得
到点
四点的距离相等?请说明理由.
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/acbfee6c40f04daf9a422c0df8122eca.png)
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/d737ba4c9fb1483eac8ddf1afc576ce4.png)
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/0c2b5d83a5964a759997cf6a715da794.png)
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/799983c3c51e4511999cf8549d3ffd0e.png)
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/a1e2a4aa0e3a4cc590044c3632d9aa57.png)
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/643569284bd64d64966623a31d56ced1.png)
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/ec455069006a45028844549f0fcd64b2.png)
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/09bff9032f2347f39639acac903b2339.png)
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/f7584886dbd74f73893d867483773b47.png)
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/6d3a6522536947ee99a1139538b7798e.png)
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/f0e78868ac7c41a4b859df22e93c4f40.png)
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/ec455069006a45028844549f0fcd64b2.png)
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/af8a61a25da14c1d8fca95dea6895514.png)
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/83efd06448e14ad2b198a62230d3e481.png)
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/9e52e53108a84129a5db459992b2fb56.png)
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/8703f1c61cd041c8b5350497a90f0a1e.png)
(1)求证:平面
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/65bca19ba6234125a9902a224ac9294a.png)
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/1982844570864da1a7383ddb2e491c85.png)
(2)求直线
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/fb297f663881439da78576a4a89f9d0c.png)
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/5b8e12b42d6b4a8fab7737b493d8ffda.png)
(3)在棱
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/78e4f64fdb3a40ff8e11d11914170911.png)
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/83b6f81eb34f4c979d0204bb86915085.png)
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/83b6f81eb34f4c979d0204bb86915085.png)
![](https://img.xkw.com/dksih/QBM/2014/1/10/1571472845512704/1571472850911232/STEM/3e3511228cc149688ee089b1eceba64f.png)
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