1 . 如图,在几何体
中,四边形
是边长为2的正方形,
,
,点
在线段
上,且
.
平面
;
(2)若
平面
,且
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/139605ce39f25ecd96cdcdad7364adb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57233d035f8df0be96001431bf009a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77e64cd7d049fd830287a6fb6b3a5870.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
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2 . 如图,
是
的直径,点
是
上的动点,过动点
的直线
垂直于
所在的平面,
,
分别是
,
的中点.
与
所在的平面的交线为
,求证:
;
(2)当
为
的中点,且
时,求
与平面
所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a392d05d3cfcbb438569b1ea9980dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4fce8e923062b9779553d6f282895b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a392d05d3cfcbb438569b1ea9980dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/820567942aa98b2feaaa017fcb7790df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd224ea30e03552a8f85d25ce787d717.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0f3703d596a2e36d6672ead47297f0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90c780dac29ff8b7df5881d3b33abab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af57d63e83ef0e183add10cd6beec65b.png)
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2023-07-14更新
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2卷引用:山东省聊城市2022-2023学年高一下学期期末数学试题
名校
3 . 在正方体
的棱长为2,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
A.直线![]() ![]() ![]() |
B.点![]() ![]() ![]() |
C.直线![]() ![]() ![]() |
D.点![]() ![]() ![]() |
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2023-02-06更新
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3卷引用:山东省聊城市莘县第一中学2022-2023学年高二上学期期末数学试题
4 . 如图(1)是一副直角三角板.现将两三角板拼成直二面角,得到四面体
,如图(2)所示,下列叙述:①
;②平面
的法向量与平面
的法向量不垂直;③异面直线
与
所成的角为
;④直线
与平面
所成的角为
.其中正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/20/f844c5fa-3952-4848-abd5-f9e017dcffe7.png?resizew=323)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2374967f2d9e2db584666703e9c9e33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7435836899f6cd9fd01d84568b02239e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9332f323c9a188e691fe9bf62083a0f8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/20/f844c5fa-3952-4848-abd5-f9e017dcffe7.png?resizew=323)
A.① | B.② | C.③ | D.④ |
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名校
5 . 如图,在三棱柱
中,点
在平面
上的射影为
的中点
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/31/255d6a1f-eeab-4b2f-ae25-1fa224296882.png?resizew=175)
(1)求证:
平面
;
(2)若
,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/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8bd8c13192ca45c16dad5d59b547220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1ac2e11788860424508ea9e80cf89d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1cb1df353c6907fec5823964eef36c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095d52314413eb48ceeeb7ac063c5b91.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/31/255d6a1f-eeab-4b2f-ae25-1fa224296882.png?resizew=175)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4890e58791814622b87c4d60ea971f54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46b4c7585238f53d85f5a96d35d95af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
您最近一年使用:0次
2022-07-18更新
|
1172次组卷
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5卷引用:山东省聊城市2021-2022学年高一下学期期末数学试题
山东省聊城市2021-2022学年高一下学期期末数学试题四川省内江市第六中学2022-2023学年高一(创新班)下学期入学考试数学试题(已下线)8.6.2直线与平面垂直的判定定理(第1课时)(精讲)(2)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)(已下线)模块四 专题2 期末重组综合练(山东)江西省萍乡市安源中学2022-2023学年高二下学期期中考试数学试题
名校
解题方法
6 . 如图,该几何体是由等高的半个圆柱和
个圆柱拼接而成,点G为弧CD的中点,且C,E,D,G四点共面.
![](https://img.xkw.com/dksih/QBM/2022/3/18/2938763061747712/2940921886441472/STEM/8c1abdcf848641e9a70083b12b585ced.png?resizew=152)
(1)证明:平面BDF⊥平面BCG;
(2)若平面BDF与平面ABG所成二面角的余弦值为
,求直线DF与平面ABF所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://img.xkw.com/dksih/QBM/2022/3/18/2938763061747712/2940921886441472/STEM/8c1abdcf848641e9a70083b12b585ced.png?resizew=152)
(1)证明:平面BDF⊥平面BCG;
(2)若平面BDF与平面ABG所成二面角的余弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83303d3784492506fc44f2b4d6b07bc1.png)
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2022-03-21更新
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1669次组卷
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16卷引用:山东省聊城市2021届高三二模联考数学试题
山东省聊城市2021届高三二模联考数学试题山东省聊城市2021届高三下学期4月高考模拟(二)(二模)数学试题湖南省长沙市长郡中学2021届高三下学期考前冲刺卷数学试题(已下线)押新高考第19题 立体几何-备战2021年高考数学临考题号押题(新高考专用)(已下线)押第19题 立体几何-备战2021年高考数学(理)临考题号押题(全国卷2)(已下线)押第18题 立体几何-备战2021年高考数学(理)临考题号押题(全国卷1)陕西省西安市西北工业大学附属中学2022届高三下学期一模理科数学试题湖北省部分重点中学2022届高三下学期4月联考数学试题(已下线)数学-2022年高考考前押题密卷(新高考Ⅰ卷)广东省茂名市2022届高三下学期调研(三)数学试题广东省佛山市南海艺术高级中学2022届高三下学期第三次大测数学试题重庆市第八中学校2022届高三下学期调研检测(十五)数学试题山东省潍坊市2022届高三下学期5月模拟数学试题(二)黑龙江省佳木斯市第八中学2023届高三第四次教学质量检测数学试题(已下线)期末模拟预测卷03(已下线)高二上学期期中【常考60题考点专练】(选修一全部内容)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)
解题方法
7 . “阿基米德多面体”也称为半正多面体,是由边数不全相同的正多边形为面围成的多面体,它体现了数学的对称美.如图,将正方体沿交于一顶点的三条棱的中点截去一个三棱锥,共截去八个三棱锥,得到的半正多面体的表面积为
,则关于该半正多面体的下列说法中正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/feefaccf-bbdf-4f89-bf54-76e43df7677e.png?resizew=137)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2c06207565e9fa6a288a788e4ab2fd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/feefaccf-bbdf-4f89-bf54-76e43df7677e.png?resizew=137)
A.与AB所成的角是60°的棱共有8条 |
B.AB与平面BCD所成的角为45° |
C.二面角![]() ![]() |
D.经过A,B,C,D四个顶点的球面面积为![]() |
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2021-07-29更新
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4卷引用:山东省聊城市2020-2021学年高一下学期期末数学试题
山东省聊城市2020-2021学年高一下学期期末数学试题(已下线)第09讲 空间点、直线、平面之间的关系(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)浙江省温州市2021-2022学年高一下学期期末模拟数学试题(B卷)(已下线)期末专题04 立体几何小题综合-【备战期末必刷真题】
名校
8 . 如图,在直三棱柱
中,底面三角形
为直角三角形,其中
,
,
,
,
,
分别为
和
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/874424e2-76ab-4747-8bff-c13ed965b398.png?resizew=163)
(1)求证:
平面
;
(2)当点
在线段
上移动时,求直线
与平面
所成角正弦的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686e0e87d8dc1da1a2a1631719e9c61b.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/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/874424e2-76ab-4747-8bff-c13ed965b398.png?resizew=163)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00c25c4259d935d6e6fabe5c3fc1f43c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae80f09dae8acbe1e5e27bd5c4d8164.png)
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4df5845bc756fe9d1a8af6bb56fcc36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ffc7d1af9053b027cf9e726f5367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
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2021-05-08更新
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3卷引用:山东省聊城第一中学2021届高三数学冲刺预测打靶试题(一)
山东省聊城第一中学2021届高三数学冲刺预测打靶试题(一)山东省青岛市2021届高三二模数学试题(已下线)专题03 立体几何中的动点问题和最值问题-【重难点突破】2021-2022学年高二数学上册常考题专练(人教A版2019选择性必修第一册)
名校
9 . 如图,在正四棱柱
中,
,点
为线段
上一动点,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/2021/1/25/2643910170001408/2646011618631680/STEM/ef1ba36b5b934b479fdfb47ee24f15ac.png?resizew=178)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f21c7c194c5bc2986a21fd441c81495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://img.xkw.com/dksih/QBM/2021/1/25/2643910170001408/2646011618631680/STEM/ef1ba36b5b934b479fdfb47ee24f15ac.png?resizew=178)
A.直线![]() ![]() |
B.三棱锥![]() ![]() |
C.三棱锥![]() ![]() |
D.直线![]() ![]() ![]() |
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2021-01-28更新
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7卷引用:山东省聊城市2020-2021学年高三上学期期末数学试题
山东省聊城市2020-2021学年高三上学期期末数学试题山东省济南市2020-2021学年高三上学期期末数学试题江苏省南京五中2021届高三下学期一模热身测试数学试题(已下线)“8+4+4”小题强化训练(33)空间几何体及其表面积、体积-2022届高考数学一轮复习(江苏等新高考地区专用)江苏省盐城市响水中学2022-2023学年高三上学期开学测试数学试题江苏省常州市第三中学等八校2022-2023学年高三上学期10月联考数学试题海南省农垦中学2023-2024学年高二上学期第一次月考数学试题
名校
解题方法
10 . 如图,设E,F分别是正方体
的棱
上两点,且
,
,则下列说法中正确的是( )
![](https://img.xkw.com/dksih/QBM/2020/6/22/2490376045346816/2490808207130624/STEM/0bb46df4ad7d4e26aa235b18e0a45251.png?resizew=215)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
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A.异面直线![]() ![]() ![]() |
B.三棱锥![]() |
C.平面![]() ![]() ![]() |
D.直线![]() ![]() ![]() |
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2020-06-23更新
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1199次组卷
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5卷引用:山东省高唐县第一中学2019-2020学年下学期第二次月考高一数学试题