名校
解题方法
1 . 已知正四面体
,点E、F分别为棱CD、AC的中点,点M为线段EF上的动点,设
,则下列说法不正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/cc09667b-1b2e-419a-b8de-88b8c86553b0.png?resizew=172)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446983c2905a9a039e04eb6541fc2b2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c8e773bffdc3689f89c11c52c68b23a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/cc09667b-1b2e-419a-b8de-88b8c86553b0.png?resizew=172)
A.直线DA与直线MB所成角随x的增大而增大 |
B.直线DA与直线MB所成角随x的增大而减小 |
C.直线DM与平面ABD所成角随x的增大而增大 |
D.直线DM与平面ABD所成角随x的增大而减小 |
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4卷引用:浙江省温州市瑞安市第六中学2021-2022学年高一下学期5月月考数学试题
2 . 如图,三棱柱
的各棱长均为2,侧棱
与底面
所成的角为60°,
为锐角,且侧面
底面
,下列四个结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/6933b759-da17-44cc-ae41-490fcf2407dc.png?resizew=183)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7647d98a828345e76f49a9afd9389850.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a2e10a5aebe40a9018d5ee3ade7af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/6933b759-da17-44cc-ae41-490fcf2407dc.png?resizew=183)
A.![]() | B.![]() |
C.直线![]() ![]() | D.![]() |
您最近一年使用:0次
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3卷引用:浙江省台州市路桥区东方理想学校2020-2021学年高一下学期5月月考数学试题
3 . 如图,四棱台
的底面是矩形,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/330172c3-fed6-4ee4-9556-efc2ee288b50.png?resizew=171)
(1)证明:
平面
;
(2)设平面
与平面
的交线为
,求直线
与平面
所成角的正弦值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a0c3a4e61b97fa9bc58f3179fc2958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a0247cb8022f81d0897142a537ddbea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43e9effc506d0373565c4394a6cf4e7f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/330172c3-fed6-4ee4-9556-efc2ee288b50.png?resizew=171)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adbe5de909b009cd31d076b19faa579f.png)
(2)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5c7bf9276315761b0b5517e2472e79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a39cf1a9eedda28c63f13ea478ec6b.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/67ee01e28681b584f85c8875f053b77b.png)
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2021-08-11更新
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2卷引用:浙江省温州市瑞安市第六中学2021-2022学年高一下学期5月月考数学试题
名校
4 . 如图,在三棱锥
中,
,
为
的中点
![](https://img.xkw.com/dksih/QBM/2021/6/14/2742660929912832/2782263620673536/STEM/b79e6b5a-8327-4f69-ab38-18094a821c0d.png?resizew=187)
(1)证明:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787ac5e13622afab5e9f8603afe42356.png)
(2)若点
为
的中点,求
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2aaed1e9ead175f30f7130569d0411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e016f7a64d3b7d1f8f802c8b9839ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://img.xkw.com/dksih/QBM/2021/6/14/2742660929912832/2782263620673536/STEM/b79e6b5a-8327-4f69-ab38-18094a821c0d.png?resizew=187)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ad334c6d980f01aaa3bf6be547a7fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787ac5e13622afab5e9f8603afe42356.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d260c4df7b0dc180af6980d21f3371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8869a52b7ac41487a4f453c19ae1361.png)
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2卷引用:浙江省Z20名校联盟(名校新高考研究联盟)2021-2022学年高三上学期第一次联考数学试题
解题方法
5 . 如图,在正方体
中,
与平面
所成的角为
,
与
所成的角为
,则
( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/bf60427f-01a8-484e-b7ae-01ca83589c1b.png?resizew=170)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c634aa65493615fbb40f1352a88c5aa3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/bf60427f-01a8-484e-b7ae-01ca83589c1b.png?resizew=170)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4卷引用:浙江省杭州市富阳区实验中学2021-2022学年高二下学期3月月考数学试题
浙江省杭州市富阳区实验中学2021-2022学年高二下学期3月月考数学试题(已下线)考点32 直线、平面垂直的判定及其性质-备战2022年高考数学一轮复习考点帮(浙江专用)山东省枣庄市2020-2021学年高一下学期期末数学试题(已下线)第九章 立体几何专练8—线面角小题2-2022届高三数学一轮复习
名校
解题方法
6 . 如图,已知在四棱锥
中,底面
是平行四边形,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/7/8/2759928229675008/2778072464392192/STEM/471852aa040247cf9c83a6cac75df133.png?resizew=304)
(Ⅰ)求
与平面
所成的角的正弦值;
(Ⅱ)棱
上是否存在点
,使得平面
平面
?若存在,求
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cbcca4833089c4f3888652028f65e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42eb1dc98ca2d830987350cb56078e8.png)
![](https://img.xkw.com/dksih/QBM/2021/7/8/2759928229675008/2778072464392192/STEM/471852aa040247cf9c83a6cac75df133.png?resizew=304)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
(Ⅱ)棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72aaf3dd6430012945b647bdb51042c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fddbb7f29e8672f34941fe70b0a1e45f.png)
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5卷引用:浙江省衢州市开化中学2021-2022学年高一下学期5月教学检测数学试题
名校
7 . 在正方体
中,点
为线段
上一动点,则( )
![](https://img.xkw.com/dksih/QBM/2021/7/9/2760371613523968/2766931253534720/STEM/286d632b-d0b2-45b8-a9b6-d7dc1b19db82.png?resizew=228)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://img.xkw.com/dksih/QBM/2021/7/9/2760371613523968/2766931253534720/STEM/286d632b-d0b2-45b8-a9b6-d7dc1b19db82.png?resizew=228)
A.对任意的点![]() ![]() |
B.三棱锥![]() |
C.当![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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5卷引用:浙江省湖州中学2021-2022学年高一下学期第二次质量检测数学试题
浙江省湖州中学2021-2022学年高一下学期第二次质量检测数学试题山东省烟台市招远市招远第一中学2020-2021学年高一下学期期末数学试题山东省烟台市2020-2021学年高一下学期期末数学试题(已下线)第8章 立体几何初步(压轴30题专练)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)(已下线)高一数学下学期期末精选50题(压轴版)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)
20-21高一下·浙江·期末
名校
8 . 如图,在四棱锥
中,
为正三角形,底面
为直角梯形,
,
,
,点
分别在线段
和
上,且
.
(1)求证:
平面
;
(2)设二面角
大小为
,若
,求直线
和平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4795ee1f96b430529934e2231b38885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bf2760931f4ed8f9fe0c87925c6b09c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c4e32e152097c2dfad9769da74680b6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/5/f14f9c8a-04b8-4a05-8b73-a093eb6cffcf.png?resizew=193)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6df63f3acea256c6518ea0bb07be17e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfaf581b4f42a25087f7eee23a7d66b6.png)
(2)设二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b796bbaeb8450404c2d146283562006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0ac75c15c00a048e6f7afc8e696f57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
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7卷引用:浙江省南太湖联盟2022-2023学年高二上学期9月联考数学试题
浙江省南太湖联盟2022-2023学年高二上学期9月联考数学试题(已下线)【新东方】在线数学170高一下湖南省长沙市长郡中学2020-2021学年高一下学期期末数学试题(已下线)一轮复习大题专练51—立体几何(线面角3)—2022届高三数学一轮复习(已下线)专题8.18 立体几何初步全章综合测试卷(提高篇)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)(已下线)第10讲空间直线、平面的平行(核心考点讲与练)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)(原卷版)贵州省铜仁第一中学2023-2024学年高二上学期8月摸底衔接质量检测(三)数学试题
9 . 如图,四棱锥
,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/1943276e-4c83-4eca-96eb-acea43c76d70.png?resizew=204)
(1)证明:
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa1162d5481e2441fe5bc0d49a576b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce35ed5c80e4d7091d73aa94b420ec11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd3eb538f36e6e722e4ce125266b99b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96ee7262d0b5cbbade014e07e7373501.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/1943276e-4c83-4eca-96eb-acea43c76d70.png?resizew=204)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed66431681da1db8f7cb0f40cd19201.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
名校
10 . 如图所示,已知
与
所在平面互相垂直,
,
,
,
,点
分别在边
上,沿直线
将
翻折,使D与A重合.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/240300b0-4447-4b57-8d61-45c3f17fa359.png?resizew=194)
(1)证明
.
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57fdd2a3642716fcf5100011eb3ec88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3bbe4cdd2c154bd9a8073b0d4cecb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbeb8ebe198bb9ef37b5c57027b28821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eb0c11e4b7aa9030a6691aee35eed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecd3355d3bee7e168af3bec0662b7dd8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/240300b0-4447-4b57-8d61-45c3f17fa359.png?resizew=194)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b182ff664d8ed9d0c518dbbf98ef10f.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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2021-03-22更新
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3卷引用:浙江省宁波十校2021届高三下学期3月联考数学试题