如图,在直三棱柱
中,
,
,
,连接
.求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a2f742c0e58984e021e3b62d22b1b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/130b2a855b0cd833fb2f62440568a322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211ad5a06b505b8365a62c1946f3cb7.png)
22-23高一下·全国·单元测试 查看更多[3]
第十一章 立体几何初步B卷 能力提升单元达标测试卷(已下线)8.5.2 直线与平面平行-同步题型分类归纳讲与练(人教A版2019必修第二册)(已下线)6.4.1直线与平面平行-【帮课堂】(北师大版2019必修第二册)
更新时间:2023-07-29 16:39:07
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【知识点】 证明线面平行
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【推荐1】求证:过平面内一点的直线平行于与该平面平行的一条直线,那么这条直线在该平面内.
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【推荐2】如图,四边形
是矩形,平面
平面
,
为
的中点,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/0be11ea8-5a6f-4c16-9113-ae5c34bc3009.png?resizew=287)
(1)在直线
上是否存在一点
,使得
平面
?若存在,试确定点
的位置并证明,若不存在,请说明理由;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb01d2b57580731c8b807ac8cffc8ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a566b100fb2ebe3d208f9b6527934218.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc39144b305c67d44410d41053a1d28.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/0be11ea8-5a6f-4c16-9113-ae5c34bc3009.png?resizew=287)
(1)在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0457394ce4f2dc8d940c565c94dcf557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20af148464904e21f4374cc8fb886fba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa3254460ecbacecb3e57c5dce227f4.png)
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【推荐3】如图,在棱长为2的正方体
中,E为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/62654cb0-0cdb-4014-b490-60f3c3454266.png?resizew=156)
(1)求证:
平面
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/62654cb0-0cdb-4014-b490-60f3c3454266.png?resizew=156)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5830646a912c3a916beac4f88c116b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
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