1 . 在立体几何探究课上,老师给每个小组分发了一个正四面体的实物模型,同学们在探究的过程中得到了一些有趣的结论.已知直线
平面
,直线
平面
,F是棱BC上一动点,现有下列四个结论:
①若M,N分别为棱AC,BD的中点,则直线
平面
;
②在棱BC上存在点F,使AF⊥平面
;
③当F为棱BC的中点时,平面
平面
;
④平面
与平面BCD所成锐二面角的正切值为
.
其中所有正确结论的编号是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/bf1a5652-1840-4be2-afa1-07146d035808.png?resizew=161)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5edfe97aeab0cf16b40fa9d2e15f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08f8b463fcecf0a757f386db56e074d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
①若M,N分别为棱AC,BD的中点,则直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
②在棱BC上存在点F,使AF⊥平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
③当F为棱BC的中点时,平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d62d30d732c3c6ee3f0dd66d7059356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
④平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
其中所有正确结论的编号是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/bf1a5652-1840-4be2-afa1-07146d035808.png?resizew=161)
A.①② | B.①③ | C.②④ | D.③④ |
您最近一年使用:0次
2021-11-28更新
|
542次组卷
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3卷引用:贵州省毕节市金沙县2022届高三11月月考数学(理)试题
解题方法
2 . 如图,在四棱锥S一ABCD中,底面ABCD是边长为2的正方形,平面SCD⊥平面ABCD,SD=SC=
.
![](https://img.xkw.com/dksih/QBM/2021/4/2/2691248154705920/2808801495449600/STEM/34620e7f-341a-4da7-a54f-ccfb9f8f7a3a.png?resizew=288)
(1)证明:BC⊥SD;
(2)求二面角A-SC-D的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839c7616cd0d90265f4b2c9c021254fe.png)
![](https://img.xkw.com/dksih/QBM/2021/4/2/2691248154705920/2808801495449600/STEM/34620e7f-341a-4da7-a54f-ccfb9f8f7a3a.png?resizew=288)
(1)证明:BC⊥SD;
(2)求二面角A-SC-D的大小.
您最近一年使用:0次
3 . 【阅读材料】数学命题的推广是数学发展不可缺少的一种手段,同时也是一项富有挑战性和创造性的活动.我们知道,在
中,记角
,
,
的对边分别为
,
,
,边与角的关系满足正弦定理:
.下面是正弦定理在空间中的一种推广:在对棱分别相等的三棱锥中,侧棱和其所对二面角的正弦值之比相等.如:在三棱锥
中,若
,
,
,记
所对的二面角
的大小为
,
所对的二面角
的大小为
,
所对的二面角
的大小为
.满足:
.根据以上阅读材料,解答以下两个问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/2f1d33af-f7b7-49c4-b51a-901a8339f463.png?resizew=320)
(1)正四面体
中,已知棱长
,二面角
的大小为
,求
的值;
(2)已知长方体
中,
,
,容易得出:平面
平面
,求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1501d4035822b34fcc2378f1e316f159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1703c9549330198bccb64a1d226eae32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5340b90363396143e0010c633a93dbf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54c12c6d0a5317038ac3eed0c32c656e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ca12f11f39405a6a49042c5e294862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec2524be492bca0d1566bf848066f10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1854ba6cc92481d7a616bd2788a47e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d1619c9a782aea7623c69f4f49492a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/2f1d33af-f7b7-49c4-b51a-901a8339f463.png?resizew=320)
(1)正四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca6d1c5eace748465b2dad5065f5111c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b61c9ab9f37d54b40107bcde9bbe22d.png)
(2)已知长方体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ef8866ccf160ddc441bf69c5d3a3d5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0fbd88fdb064072eedd136e9cb41ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73845d4d663b3de0b281611fe2c762fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d4cc3c81b7ce3ce201a25394234276.png)
您最近一年使用:0次
解题方法
4 . 如图,D是以AB为直径的半圆O上异于A,B的点,△ABC所在的平面垂直于半圆O所在的平面,且
AB=2BC=2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/465f69e3-4ec9-4e79-91aa-bfaf224561b2.png?resizew=153)
(1)证明:AD⊥DC;
(2)若
求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a83c9ee23ab1974908dbcb6c1f8f0d52.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/465f69e3-4ec9-4e79-91aa-bfaf224561b2.png?resizew=153)
(1)证明:AD⊥DC;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1b620fb692cb5feea1ae55a24d6608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0ac3005d5ecd6d4cea0ce99a47ef3c.png)
您最近一年使用:0次
2021-02-07更新
|
163次组卷
|
2卷引用:贵州省毕节市2021届高三上学期诊断性考试数学(文)试题(一)
5 . 如图,四棱锥
的底面
是边长为
的菱形,
,已知
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/c98ba8df-b2ad-46af-84cf-3742204e142b.png?resizew=183)
(1)求证:
;
(2)求二面角
的余弦值;
(3)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b2f446cccf2652c090e99a75beb3bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d906ee0d60f3f4654fb516fe4973413.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c85aeab3aeaf4367b711da8cde2e8bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/c98ba8df-b2ad-46af-84cf-3742204e142b.png?resizew=183)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4125524caac016727c80d2722c5ba3.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db04e82f03e6216886d416b35abe85a3.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d95e78927443bbadb5bf60f1c836ea24.png)
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6 . 如图,正三棱柱
的棱长均为2,M是侧棱
的中点.
![](https://img.xkw.com/dksih/QBM/2021/1/27/2645119770124288/2646380397133824/STEM/0766a3e036e8467893520be4d4760d26.png?resizew=199)
(1)在图中作出平面
与平面
的交线l(简要说明),并证明
平面
;
(2)求平面
与平面
所成二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/2021/1/27/2645119770124288/2646380397133824/STEM/0766a3e036e8467893520be4d4760d26.png?resizew=199)
(1)在图中作出平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fed2f706801662432b68797e72647c6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9df740160690029ac1e730c85f20347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee8b5a6dbcf05f572f83f51abf7d668c.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fed2f706801662432b68797e72647c6e.png)
您最近一年使用:0次
2021-01-29更新
|
977次组卷
|
2卷引用:贵州省贵阳市2021届高三上学期期末检测考试数学(理)试题