真题
1 . 如图,在五棱锥
中,
底面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/dfed0b05-2ba1-4d10-bfd2-7041decb772b.png?resizew=163)
(1)求异面直线
与
所成的角;(用反三角函数值表示)
(2)证明:
平面
;
(3)用反三角函数值表示二面角
的大小.(本小问不必写出解答过程)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/989babd4c8db2422e5d239e03dae94b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c6a57517fb8cdbe016cdee4aa64756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7fc9b1a395ad2e2fb2b207560754dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73320c736844aaf8e0cc98542a227513.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/dfed0b05-2ba1-4d10-bfd2-7041decb772b.png?resizew=163)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
(3)用反三角函数值表示二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c53f1e79257ff52a0408fdc482488d0.png)
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名校
2 . 如图,在三棱柱
中,侧面
底面
,侧面
是菱形,
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/9/15/3066911624208384/3069728783171584/STEM/816e99ae7f7a42f7972d80daff0a6be3.png?resizew=253)
(1)若
为
的中点,求证:
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f70d708336d4f15e7fca0b26acb353b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed8f7d3d7043d4b1eb98fc5c4e2fcd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209acf15985d1ea1ad86fc4a37e38c0b.png)
![](https://img.xkw.com/dksih/QBM/2022/9/15/3066911624208384/3069728783171584/STEM/816e99ae7f7a42f7972d80daff0a6be3.png?resizew=253)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c84a436704964dc76f16c2c23665ab3c.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef20b51b960e3f06a5abc65608f5f7e.png)
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2022-09-19更新
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1822次组卷
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12卷引用:江苏省南通市2022-2023学年高三上学期第一次质量监测数学试题
江苏省南通市2022-2023学年高三上学期第一次质量监测数学试题福建省福州市屏东中学2023届高三上学期10月第一次月考数学试题安徽省芜湖市第一中学2022-2023学年高二上学期第一次阶段性诊断测试数学试题黑龙江省大庆铁人中学2022-2023学年高三上学期第一次月考数学试题浙江省温州市平阳县万全综合高级中学2022-2023学年高二上学期10月检测数学试题福建省宁德市民族中学2023届高三上学期期中考试数学试题山东省青岛第六十七中学2022-2023学年高二上学期期中数学试题福建省晋江养正中学2023届高三第一次阶段性诊断测试数学试题江西省南昌市三校(一中、十中、铁一中)2023届高三上学期第一次联考(11月)数学(理)试题贵州省贵阳清镇北大培文学校2022-2023学年高二上学期期中考试数学试题湖北省咸宁鲁迅学校2022-2023学年高三上学期10月月考数学试题山东省临沂市平邑县平邑县第一中学2023-2024学年高三上学期11月月考数学试题
3 . 如图所示,在长方体
中,
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2022/7/5/3016098087108608/3017318811435008/STEM/404f46f076bf4e94b9bd590c9c38eca6.png?resizew=224)
(1)求证:平面
平面
;
(2)求异面直线
与
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ef8866ccf160ddc441bf69c5d3a3d5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2022/7/5/3016098087108608/3017318811435008/STEM/404f46f076bf4e94b9bd590c9c38eca6.png?resizew=224)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b3e7c7845a0ec3cbac709fda131764.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd7cc5d9199856cb62ac8898664c931.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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2022-07-07更新
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3卷引用:江苏省邳州市宿羊山高级中学2021-2022学年高一下学期第二次学情检测数学试题
名校
解题方法
4 . 如图,多面体ABCEF中,
,
,D为BC的中点,四边形ADEF为矩形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/121f0a38-c4b3-4eb4-a253-7c2803fe6f54.png?resizew=168)
(1)证明:
;
(2)若
,
,
,求异面直线CE与FD所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbfc35fc915ac7d4dc017e60ccdecbe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/121f0a38-c4b3-4eb4-a253-7c2803fe6f54.png?resizew=168)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31b2cc1d0bfd22c88286880b9da1f6f4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fffa3d9c32da53b0ea0c338012ea20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a702c324e0c76150540c3d32df802077.png)
您最近一年使用:0次
2022-04-26更新
|
518次组卷
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2卷引用:第13章《立体几何初步》单元达标高分突破必刷卷(培优版)-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(苏教版2019必修第二册)
名校
解题方法
5 . 如图,四棱锥S-ABCD的底面ABCD是正方形,SD⊥平面ABCD,SD=2a,
,E是SD上的点,且
.
![](https://img.xkw.com/dksih/QBM/2022/5/10/2976276259782656/2976974820343808/STEM/e81bfbde-48a7-4ef2-be7c-bd31a1ae1a9d.png?resizew=173)
(1)求证:AC⊥BE;
(2)若点B到平面ACE的距离为
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfda7a170c4a5b5e61b3e82e4ec30110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5940069ecb7f22cca04d1d386af5def.png)
![](https://img.xkw.com/dksih/QBM/2022/5/10/2976276259782656/2976974820343808/STEM/e81bfbde-48a7-4ef2-be7c-bd31a1ae1a9d.png?resizew=173)
(1)求证:AC⊥BE;
(2)若点B到平面ACE的距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f8873277888e5c66b34ce31841d1fda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2022-05-11更新
|
3254次组卷
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4卷引用:高一下学期第二次月考(苏教版2019必修二:立体几何、平面向量、三角恒等变换、解三角形、复数)
(已下线)高一下学期第二次月考(苏教版2019必修二:立体几何、平面向量、三角恒等变换、解三角形、复数)河南省百所名校2022届普通高校招生全国统一考试猜题压轴卷文科数学试题河南省南阳市第一中学校2022届高考考前适应性考试文科数学试题山东省新泰市第一中学2021-2022学年高一下学期第二次质量检测数学试题
名校
解题方法
6 . 已知四棱锥
的底面是边长为2的菱形,
底面
.
![](https://img.xkw.com/dksih/QBM/2022/5/30/2990696686772224/2991328961732608/STEM/5542557c-a00e-4913-970f-003ef916f7e9.png?resizew=172)
(1)求证:
平面
;
(2)当
,
时,求直线
与
所成角的余弦值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2022/5/30/2990696686772224/2991328961732608/STEM/5542557c-a00e-4913-970f-003ef916f7e9.png?resizew=172)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bec03e804f0cea1db5cde2aa185056a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d6bdfb0e1be5583e794ab614a8abe1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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2022-05-31更新
|
617次组卷
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3卷引用:江苏省连云港高级中学2021-2022学年高一下学期第二次阶段测试数学试题
江苏省连云港高级中学2021-2022学年高一下学期第二次阶段测试数学试题(已下线)第02讲 玩转立体几何中的角度、体积、距离问题-【暑假自学课】2022年新高二数学暑假精品课(苏教版2019选择性必修第一册)河南省南阳市卧龙区博雅学校2022-2023学年高一下学期6月月考数学试题
名校
7 . 已知四棱锥
的底面是边长为2的菱形,
底面
.
![](https://img.xkw.com/dksih/QBM/2022/5/3/2971467522613248/2972829229432832/STEM/59d7d6e6073141fd9ad4fe4d23e58024.png?resizew=244)
(1)求证:
平面
;
(2)已知
,
(ⅰ)当
时,求直线
与
所成角的余弦值;
(ⅱ)当直线
与平面
所成的角为
时,求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2022/5/3/2971467522613248/2972829229432832/STEM/59d7d6e6073141fd9ad4fe4d23e58024.png?resizew=244)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bec03e804f0cea1db5cde2aa185056a.png)
(ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d6bdfb0e1be5583e794ab614a8abe1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(ⅱ)当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
2022-05-05更新
|
3111次组卷
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5卷引用:江苏省盐城市响水中学2021-2022学年高二下学期第二次学情分析考试数学试题
江苏省盐城市响水中学2021-2022学年高二下学期第二次学情分析考试数学试题(已下线)第02讲 玩转立体几何中的角度、体积、距离问题-【暑假自学课】2022年新高二数学暑假精品课(苏教版2019选择性必修第一册)广东省广州市白云中学2021-2022学年高一下学期期中数学试题(已下线)期末押题预测卷01广东省茂名市信宜市第二中学2022-2023学年高一下学期期末数学试题
2022高一·全国·专题练习
解题方法
8 . 如图,已知长方体ABCD-A1B1C1D1中,A1A=AB,E,F分别是BD1和AD的中点,求证:CD1⊥EF.
您最近一年使用:0次
2022-05-19更新
|
389次组卷
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9卷引用:13.2.2 空间两条直线的位置关系
(已下线)13.2.2 空间两条直线的位置关系(已下线)8.6.1直线与直线垂直(练案)-2021-2022学年高一数学同步备课 (人教A版2019 必修第二册)(已下线)第31讲 直线与直线垂直(已下线)8.6.1 直线与直线垂直(精练)(已下线)第一章 点线面位置关系 专题二 空间垂直关系的判定与证明 微点1 空间直线垂直的判定与证明【基础版】(已下线)8.6.1 直线与直线垂直【第一课】“上好三节课,做好三套题“高中数学素养晋级之路(已下线)8.6.1 直线与直线垂直-同步题型分类归纳讲与练(人教A版2019必修第二册)(已下线)8.6.1 直线与直线垂直【第二课】“上好三节课,做好三套题“高中数学素养晋级之路(已下线)11.3.1平行直线与异面直线-同步精品课堂(人教B版2019必修第四册)
9 . 如图,在多面体ABCDEF中,四边形ACDE是正方形,DF//BC,AB⊥AC,AE⊥平面ABC,AB=AC=2,EF=DF=
.
![](https://img.xkw.com/dksih/QBM/2022/2/28/2926244105977856/2929928890179584/STEM/a786b5c568ec4c3897bcaba37cad87c8.png?resizew=186)
(1)求证:平面BCDF⊥平面BEF;
(2)求二面角A-BF-E的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/2022/2/28/2926244105977856/2929928890179584/STEM/a786b5c568ec4c3897bcaba37cad87c8.png?resizew=186)
(1)求证:平面BCDF⊥平面BEF;
(2)求二面角A-BF-E的余弦值.
您最近一年使用:0次
2022-03-05更新
|
1254次组卷
|
5卷引用:江苏省南京市第一中学江北校区2024届高三上学期一模数学练习试题
名校
10 . 如图,在正方体
,
分别为线段
的中点.
![](https://img.xkw.com/dksih/QBM/2022/4/19/2961603539705856/2962770798256128/STEM/654fdced-29f7-4916-aac4-24433ec41392.png?resizew=180)
(1)求证:
平面
;
(2)求异面直线
与
的所成角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c72057b4bd74bf9f9b63b8b11f0c109.png)
![](https://img.xkw.com/dksih/QBM/2022/4/19/2961603539705856/2962770798256128/STEM/654fdced-29f7-4916-aac4-24433ec41392.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93ecad355286188fd317939fa50f9555.png)
您最近一年使用:0次
2022-04-21更新
|
856次组卷
|
2卷引用:江苏省南京市第九中学2021-2022学年高一下学期期中数学试题