名校
解题方法
1 . 已知四棱柱
的所有棱长均为2,点
为
的中点,点
为
的中点,点
为
的中点,且
,
两两垂直,过点G的平面
与直线
,
,
分别交于点
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/298cc3d9bc6dc88c494b5489ee2ca846.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96c92bc20565fb976e0c73ee4017261.png)
A.![]() |
B.平面![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.当点![]() ![]() ![]() |
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解题方法
2 . 已知菱形
如图①所示,其中
,现沿
进行翻折,使得平面
平面
,再过点B作
平面
,且
,所得图形如图②所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/13/479518e4-4e32-48b3-827b-1877a266a776.png?resizew=320)
(1)若点P满足
,且
平面
,求
的值;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c646c683fbe522edb7ea54fd3ad873d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662698361c6b3ddaf0c28a3c87be53e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d11f385a2ddc33739bb90f328614a8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/13/479518e4-4e32-48b3-827b-1877a266a776.png?resizew=320)
(1)若点P满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545b3d484d15f6e8d506133c3167822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d33288714812fc459b02153b0cbef1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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名校
解题方法
3 . 不同材质的楔形零配件广泛应用于生产生活中,例如,制作桌凳时,利用楔形木块可以防止松动,使构件更牢固.如图是从棱长为3的正方体木块中截出的一个楔形体
,将正方体的上底面平均分成九个小正方形,其中
是中间的小正方形的顶点.
(1)求楔形体的表面积;
(2)求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a767884cc717befc756750db80da9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48593b2bdb51550ec0a2b9d5893d36fe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/c961ee1b-f0f2-4aeb-8e87-fd02920fe120.png?resizew=196)
(1)求楔形体的表面积;
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1de7da3ab92e70f135ea628a691167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/820ffc2ac7c01b2873f69ce777e14026.png)
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4 . 如图1,已知正三棱锥
分别为
的中点,将其展开得到如图2的平面展开图(点
的展开点分别为
,点
的展开点分别为
),其中
的面积为
.在三棱锥
中,
(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/2a78432c0302b041c04b5f4d78cedde1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374fe9986ebbc986fc422e514ab93a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5425108c557f0f21474c045334f97d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05df617dae0d3203f02a488277e419f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2793a649954fbb40a20100114cc507f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b27567d43c5b91382ee3d7ca708ee422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/12/29faa8bd-8d34-47af-a14a-e24dd980c84d.png?resizew=246)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c5757f787d98f9a46777324b69ad672.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ce50ba5e349425274f05d46d120a74.png)
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名校
解题方法
5 . 已知空间中不共面的四点
,
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce7f3658bd6c1294df92b939dc1cde6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa6286cbeac434d7c4dab62454df522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c370d211cf6cd1bf5108294b442b16fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e224b7933a71fdfa45d7d2583a398a58.png)
A.直线![]() ![]() ![]() | B.二面角![]() ![]() |
C.点D到平面![]() ![]() | D.四面体![]() ![]() |
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2022-11-15更新
|
262次组卷
|
3卷引用:安徽省马鞍山市第二十二中学等校2022-2023学年高二上学期阶段联考数学试题
名校
6 . 如图所示为一个半圆柱,
为其轴截面,E为半圆弧
上的任意点(异于C、D两点).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/30fec032-a3ec-465a-87ff-8a610b212d37.png?resizew=195)
(1)求证:不论E在何处总有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5322a78b02c2bc387ea7dce3e9461974.png)
(2)已知
,
,
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/30fec032-a3ec-465a-87ff-8a610b212d37.png?resizew=195)
(1)求证:不论E在何处总有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5322a78b02c2bc387ea7dce3e9461974.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c659e22afc5537936ae355cd80bd690d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b0f78a8003789a66fa4cb38a84858c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a2dd80354087c6c320cce82ea6901d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f18a490a22cac27417ddc794f00a1941.png)
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