名校
解题方法
1 . 如图,已知四面体
的各条棱长均等于
分别是棱
的中点.若用一个与直线
垂直,且与四面体的每一个面都相交的平面
去截该四面体,由此得到一个多边形截面
,当截面
面积最大时,四棱锥
的体积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2612d8c87010adfe87728a591b63e3a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d93949d8a15aca4e79cedb978590571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a315e4b5963127bf8550cde03ca1966d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a315e4b5963127bf8550cde03ca1966d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df6a9fadc944f228ec12642a194f35e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/17/50b73dc0-268c-4c34-bdb4-8ac147cdf3e5.png?resizew=168)
您最近一年使用:0次
名校
2 . 如图,在三棱柱
中,
分别为
的中点,则下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c2d86d8daea5e652d99fe1c6bc3f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c21840e2f00fe67676dd3a90a40dd3a.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-04-06更新
|
3436次组卷
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10卷引用:福建省三明第一中学2023-2024学年高一下学期期中考试数学试卷
福建省三明第一中学2023-2024学年高一下学期期中考试数学试卷湖南省新高考教学教研联盟2024届高三下学期第二次联考数学试题(已下线)8.4.1 平面【第三课】“上好三节课,做好三套题“高中数学素养晋级之路四川省成都市成华区某校2023-2024学年高三“三诊”数学(文)试题海南省海南中学2023-2024学年高一下学期期中考试数学试题黑龙江省大庆市实验中学实验二部2023-2024学年高三下学期阶段考试数学试题广东省茂名市高2024届高三下学期高考模拟数学试题河南省信阳高级中学2023-2024学年高一下学期5月期中考试数学试题(已下线)第8.4.1讲 平面-同步精讲精练宝典(人教A版2019必修第二册)湖北省荆州市荆州中学2023-2024学年高一下学期5月月考数学试卷
名校
解题方法
3 . 正方体
中,
,
是
的中点,下列说法中错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5a64bcb77f5f64e4af6930c249a270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
A.![]() ![]() |
B.异面直线![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.过![]() ![]() ![]() ![]() ![]() |
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2023-12-24更新
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4卷引用:福建省三明市尤溪县第七中学2023-2024学年高一下学期期中考试数学试题
4 . 如图,在正四棱锥
中,
,
,
分别是
,
的中点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03c97a79520fa792cf5eaf209f6c8e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/9/c384b5ca-0dff-4b43-998f-7f36ff842a34.png?resizew=192)
A.![]() | B.直线![]() ![]() ![]() |
C.点![]() ![]() ![]() | D.点![]() ![]() |
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2023-09-07更新
|
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8卷引用:福建省永安市第九中学2023-2024学年高二上学期第一次月考测试数学试题
福建省永安市第九中学2023-2024学年高二上学期第一次月考测试数学试题山西省金科大联考2023-2024学年高二上学期开学考试数学试题河北省沧州市运东七县联考2023-2024学年高二上学期10月月考数学试题浙江省杭州市富阳区实验中学2023-2024学年高二上学期9月摸底考试数学试题湖北省鄂州市部分高中教科研协作体2023-2024学年高二上学期11月期中考试数学试题河北省石家庄第十五中学2023-2024学年高二上学期期中数学试题湖南省株洲市第二中学2021-2022学年高一下学期第三次月考数学试卷(已下线)第二章 立体几何中的计算 专题二 空间距离 微点1 空间两点间的距离、点到直线的距离【培优版】
名校
5 . 已知正三棱柱木料
各棱长都为2,如图所示,
,
分别为
和
的中心,
为线段
上的点,且
,过
三点的截面把该木料截成两部分,则截面面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0a4f38420bb9215dbc9c875b755838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba473b73e5fe7c07da4bc796e3c3f27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b96d93615b03284ada76153c394a49d.png)
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2023-07-27更新
|
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6卷引用:福建省三明市2022-2023学年高一下学期期末质量检测数学试题
福建省三明市2022-2023学年高一下学期期末质量检测数学试题(已下线)8.4.1平面(已下线)11.2平面的基本事实与推论-同步精品课堂(人教B版2019必修第四册)(已下线)专题04 立体几何初步-期期末真题分类汇编(人教A版2019必修第二册)福建省泉州市安溪蓝溪中学2023-2024学年高一下学期第二次阶段检测(6月)数学试卷福建省宁德市福安市第一中学2023-2024学年高一下学期第三次月考数学试题
名校
解题方法
6 . 如图,在几何体
中,平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
平面
平面
,底面
为直角梯形.
为
的中点,
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/15/1d5a18c3-8fd0-45de-82bc-51a204c3ae9c.png?resizew=182)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc81d42ad20eb0b0ca0807e5a4c3ceb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e757f79f7d80369bb32cffe476c57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5a7cfed77121d5b0014c3487214fa59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/418b8c097da01831eb9efa8634689d26.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/15/1d5a18c3-8fd0-45de-82bc-51a204c3ae9c.png?resizew=182)
A.![]() | B.![]() |
C.![]() ![]() ![]() | D.几何体![]() |
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2023-05-13更新
|
462次组卷
|
2卷引用:福建省三明市永安第九中学2022-2023学年高一下学期5月月考数学试题
名校
7 . 如图,已知四棱锥
的底面为菱形,
,
,
,
为
的中点,
为
的中点,平面
过
、
、
三点且与面
交于直线
,
交
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/2/98b0fd5c-9639-4d42-9af1-b44b6f9b4792.png?resizew=235)
(1)求证:面
面
;
(2)求证:
;
(3)求平面
与平面
所成夹角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19e0ba32fcadd4114a3c52b52c3aea23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14f698605a196cf83ccba6a601d0e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/2/98b0fd5c-9639-4d42-9af1-b44b6f9b4792.png?resizew=235)
(1)求证:面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8dd986a065e339b1b821830781d7a0.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6760f565c694d1cdb6d7068e14526d00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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名校
解题方法
8 . 如图,正三棱锥
和正三棱锥
的侧棱长均为
,
.若将正三棱锥
绕
旋转,使得点
分别旋转至点
处,且
四点共面,点
分别位于
两侧,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/1/10b6472e-d579-47dc-9207-1c98e464856b.png?resizew=137)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf9718967af7a01c5b4866ea6f73bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f2d2ef6661d1808fed0cbd1b0fa53d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf9718967af7a01c5b4866ea6f73bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff571c72c041d8668b4d2754679f64d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de83ce4d5ad4bb47d74cbd3bc3394ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e5d9f7e63d80a1969318ac999a3e6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e925a4d4d706168d1ae69167483096c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/1/10b6472e-d579-47dc-9207-1c98e464856b.png?resizew=137)
A.![]() |
B.![]() ![]() |
C.二面角![]() ![]() |
D.多面体![]() ![]() |
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2023-04-26更新
|
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3卷引用:福建省三明第一中学2022-2023学年高一下学期期中考试数学试题
福建省三明第一中学2022-2023学年高一下学期期中考试数学试题(已下线)高一数学下学期第二次月考02(范围:平面向量,解三角形,复数,立体几何)江苏省盐城市五校2022-2023学年高一下学期5月联考数学试题
名校
解题方法
9 . 正四棱柱
中,
,则异面直线
与
所成角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7a724f22477766879d1e103e5a6c0b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-06-21更新
|
689次组卷
|
4卷引用:福建省三明市尤溪县第五中学等两校2021-2022学年高一下学期期中联考数学试题
10 . 如图,在长方体木料
中,
,
为棱
的中点.
(1)如图(1),求直线
与平面
所成角的正弦值.
(2)如图(2),要过点
和棱
将木料锯开.
①在木料表面画出符合要求的线,写出作图过程并说明理由;
②写出切割后体积较大的几何体的名称,并求出它的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f7ad41c55fab640a159a08a12c6b03c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/27/b7bbf9a1-e643-455c-b16b-d49c69a9b6b4.png?resizew=375)
(1)如图(1),求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb04914c4e8fb3483da44c67fe1809f.png)
(2)如图(2),要过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
①在木料表面画出符合要求的线,写出作图过程并说明理由;
②写出切割后体积较大的几何体的名称,并求出它的体积.
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