如图,在三棱锥
中,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/70dbb32d-136e-4af7-88e5-0b5bbb9957fb.png?resizew=165)
(1)证明:平面
平面
;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f55595e4f115fa46068eb11c866386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ad8d16722f5b9e7fd2602f14d5ffbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c3103663072a4e76f465aa2b6d83601.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3bbe4cdd2c154bd9a8073b0d4cecb8a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/70dbb32d-136e-4af7-88e5-0b5bbb9957fb.png?resizew=165)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c079889aea502b5783046f78728eb1.png)
更新时间:2022-03-23 15:50:06
|
相似题推荐
解答题-证明题
|
较易
(0.85)
解题方法
【推荐1】如图,
是棱长为
的正方体.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712253541916672/2717113461465088/STEM/4ec4d59b-2b46-406a-8557-b47ee8808d09.png?resizew=242)
(1)求证:平面
平面
;
(2)点
是棱
上一动点,过点
作平面
平行底面
,
为多长时,正方体
在平面
下方的部分被平面
截得的两部分的体积比是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712253541916672/2717113461465088/STEM/4ec4d59b-2b46-406a-8557-b47ee8808d09.png?resizew=242)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0fbd88fdb064072eedd136e9cb41ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5881f1ce9b4172ca346032d0fd1e3d.png)
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解题方法
【推荐2】如图,在四棱锥
中,
,
,连接
.
平面
;
(2)求直线
与平面
所成角正弦值的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89bfb045696b5318bc0e5f9cc986a497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6316e6bfd2d1831ecd08238797f8123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2626a034d2894bd70aa5136f87c7774b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a26a7784c7419d8359fb119c8ecc03d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9068f29d671d76d1e95ba3a4eaff5b96.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
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解答题-问答题
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【推荐1】四棱锥
中,
平面
,
,
,
,
是
的中点.
(1)证明:
平面
;
(2)求平面
与平面
所成二面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6deecf9ccb7b7879455050633219e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0adacf7dd66e80f720da4bcfe91c022d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b78172568aac9805d2ea2d5f742bf80c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d923a338dd2d2e29336b42574d38448.png)
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【推荐2】在长方体
中,E,F分别是棱BC,CC1上的点,CF=AB=2CE,AB∶AD:AA1=1∶2∶4
![](https://img.xkw.com/dksih/QBM/2021/12/26/2880413898670080/2886708501798912/STEM/b622fed7-470c-4088-864e-0cfec6ce3f42.png?resizew=171)
(1)求异面直线EF,A1D所成角的余弦值;
(2)证明∶AF⊥平面
;
(3)求二面角A-ED-F正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/2021/12/26/2880413898670080/2886708501798912/STEM/b622fed7-470c-4088-864e-0cfec6ce3f42.png?resizew=171)
(1)求异面直线EF,A1D所成角的余弦值;
(2)证明∶AF⊥平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c9f260496ba23993238601a89eca5c.png)
(3)求二面角A-ED-F正弦值.
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