名校
解题方法
1 . 如图甲,在直角三角形
中,已知
,
,
,D,E分别是
的中点.将
沿
折起,使点A到达点
的位置,且
,连接
,得到如图乙所示的四棱锥![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2792f6f1fde407c93201c0f3fad39d52.png)
,M为线段
上一点.
![](https://img.xkw.com/dksih/QBM/2021/12/27/2881711704768512/2883062489751552/STEM/fec3dcb7-0cff-40c0-b9e1-a756f6dfb4bb.png?resizew=286)
(1)证明:平面
平面
;
(2)过B,C,M三点的平面与线段A'E相交于点N,从下列三个条件中选择一个作为已知条件,求直线DN与平面A'BC所成角的正弦值.
①
;②直线
与
所成角的大小为
;③三棱锥
的体积是三棱锥
体积的![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c77a22740bd1ad5f5979e4579cb177d0.png)
注:如果选择多个条件分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4772895af07cae75fc85a48507952c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea7b7e2f8b77c8a8518198511b458233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2792f6f1fde407c93201c0f3fad39d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1333acc72211e3ddb9a0f8c726ce8a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a21897349d3d7c94419692106887153.png)
![](https://img.xkw.com/dksih/QBM/2021/12/27/2881711704768512/2883062489751552/STEM/fec3dcb7-0cff-40c0-b9e1-a756f6dfb4bb.png?resizew=286)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789069cf57bd1059f5e0f9ac61d933b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1333acc72211e3ddb9a0f8c726ce8a5.png)
(2)过B,C,M三点的平面与线段A'E相交于点N,从下列三个条件中选择一个作为已知条件,求直线DN与平面A'BC所成角的正弦值.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7f8da1f66714eba7f2867a19d02479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee48b4d6b9ee347b2ba6305f2fdc2bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04aab7c8fe102e94d113cad242921a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c77a22740bd1ad5f5979e4579cb177d0.png)
注:如果选择多个条件分别解答,按第一个解答计分.
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2021-12-29更新
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3卷引用:四川省成都市2021-2022学年高三第一次诊断性检测理科数学试题