名校
1 . 如图,在四棱锥
中,底面
是边长为2的正方形,
平面
,
是
中点,
是
中点.
平面
;
(2)若
,求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92fd5389b546fe1c72c01fd514f4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9d925daead2e318ad5e54fd3e4441a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c5a4dfcf4c24a8ecb210cc4c53db221.png)
您最近一年使用:0次
2 . 如图,在正方体
中,
为棱
上的动点,
为棱
的中点,则下列选项正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/2c0ee227-5216-4db2-afbe-d0dfac65798b.png?resizew=166)
![](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/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/2c0ee227-5216-4db2-afbe-d0dfac65798b.png?resizew=166)
A.直线![]() ![]() |
B.三棱锥![]() |
C.当![]() ![]() ![]() ![]() ![]() |
D.存在点![]() ![]() ![]() |
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3 . 如图,边长为4的两个正三角形
,
所在平面互相垂直,E,F分别为BC,CD的中点,点G在棱AD上,
,直线AB与平面
相交于点H.
;②直线HE,GF,AC相交于一点;
注:若两个问题均作答,则按第一个计分.
(2)求直线BD与平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a100d3638f0f04db2bd262c051f59b2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e011e5a622d961d9174ebce34c6ee033.png)
注:若两个问题均作答,则按第一个计分.
(2)求直线BD与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
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2024-03-21更新
|
2129次组卷
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6卷引用:江苏省扬州市2024届高三第二次调研测试数学试题
江苏省扬州市2024届高三第二次调研测试数学试题江苏省南通市2024届高三第二次调研测试数学试题江苏省泰州市2024届高三第二次调研测试数学试题(已下线)模块三 专题3 高考新题型专练 专题1 劣构题专练(苏教版)(已下线)江苏省南通市2024届高三第二次调研测试数学试题变式题 16-19(已下线)江苏省泰州市2024届高三第二次调研测试数学试题变式题16-19
名校
解题方法
4 . 已知正方体
的棱长为
,点
分别是棱
,
的中点,点
是侧面
内一点
含边界
若
平面
,则下列说法正确的有( )
A.点![]() | B.三棱锥![]() |
C.![]() ![]() | D.直线![]() ![]() ![]() |
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2024-03-01更新
|
639次组卷
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3卷引用:江苏省高邮市2024届高三下学期期初学情调研测试数学试题
江苏省高邮市2024届高三下学期期初学情调研测试数学试题(已下线)第三章 空间轨迹问题 专题六 立体几何轨迹中的范围、最值问题 微点1 立体几何轨迹中的范围、最值问题【培优版】江苏省连云港高级中学2023-2024学年高二下学期第一次月考数学试卷
名校
解题方法
5 . 刍薨是《九章算术》中出现的一种几何体,如图所示,其底面为矩形,顶棱
和底面平行,书中描述了刍薨的体积计算方法:求积术曰,倍下袤,上袤从之,以广乘之,又以高乘之,六而一,即
(其中
是刍薨的高,即顶棱
到底面
的距离),已知
和
均为等边三角形,若二面角
和
的大小均为
,则该刍薨的体积为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-12-29更新
|
756次组卷
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4卷引用:江苏省扬州市扬州中学2024届高三上学期1月阶段性检测数学试题
江苏省扬州市扬州中学2024届高三上学期1月阶段性检测数学试题河北省金科大联考2024届高三上学期12月月考数学试题福建省百校联考2024届高三上学期12月月考数学试题(已下线)第八章 立体几何初步(二)(知识归纳+题型突破)(2)-单元速记·巧练(人教A版2019必修第二册)
名校
6 . 如图,在四棱锥
中,
,设
分列为棱
的中点.
平面
;
(2)若
,求
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/65ea63588ceef54b569a96707b4cf140.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b094411c562930ff2d67b582cfd48cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc419a9ba7b9da8208d57d7d3ed808ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c745df4f226027778d5fe45b6501b822.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e5a421ad7b87d395848c696f3ff7426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2023-12-29更新
|
824次组卷
|
4卷引用:江苏省扬州市扬州中学2024届高三上学期1月阶段性检测数学试题
名校
7 . 如图所示的几何体 ABCDE 中,DA⊥平面 EAB ,AB=AD=AE=2BC=2,
M是EC上的点(不与端点重合),F 为AD上的点,N 为BE的中点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098727ac4cf2487aef9b04066eab15cc.png)
(i) 求证:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af29254fe60a392c249c5791279e9c8.png)
(ii) 求点F 到平面MBD的距离.
(2)若平面MBD与平面ABD所成角(锐角)的余弦值为
试确定点M在EC上的位置.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27fc83ab13e367074de997e7e226a403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098727ac4cf2487aef9b04066eab15cc.png)
(i) 求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d53d5c96de34fcf95794e51c2761b671.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af29254fe60a392c249c5791279e9c8.png)
(ii) 求点F 到平面MBD的距离.
(2)若平面MBD与平面ABD所成角(锐角)的余弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7207646d70b9977b0b21802f516dd2ea.png)
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2023-12-18更新
|
257次组卷
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4卷引用:江苏省扬州市广陵区红桥高级中学2023-2024学年高二下学期3月月考数学试题
江苏省扬州市广陵区红桥高级中学2023-2024学年高二下学期3月月考数学试题天津市和平区耀华中学2023-2024学年高二上学期12月月考数学试题(已下线)第6章 空间向量与立体几何单元综合测试卷-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第二册)江苏省泰州市第三高级中学2023-2024学年高二下学期第一次阶段检测数学试卷
名校
8 . 如图,在四棱锥
中,
底面
,
,
.点
在棱
上,
,点
在棱
上,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/a7c0954c-5ea5-4e29-bdfd-1ec5f7763684.png?resizew=162)
(1)若
,
为
的中点,求证:
平面
;
(2)若直线
与平面
所成角的正弦值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4eebde0291ae62d02a498b56358ece.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0c805a8179966c0b486f4117605090f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/a7c0954c-5ea5-4e29-bdfd-1ec5f7763684.png?resizew=162)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be5dc953c41ce0ffe6eb8d95e6ef1256.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a158113467436c24c6db00f058cf91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ae8a3c30480b46d1cb81cf5745f2ae.png)
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2023-12-15更新
|
169次组卷
|
2卷引用:江苏省扬州市广陵区红桥高级中学 2024届高三上学期12月月考数学试题
名校
9 . 如图,直四棱柱
中,底面
为等腰梯形,其中
,
,
,
,N为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/31/51be6784-d6ab-4053-92ee-9b42b259b401.png?resizew=157)
(1)若平面
交侧棱
于点P,求证:
,并求出AP的长度;
(2)求平面
与底面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/0cad8b2d5a892c557a5bc7650bf4dcb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27db558e8db4c957654c8e5cecd2d2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4771a646e2d9895a2d4e44184ca0c558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/31/51be6784-d6ab-4053-92ee-9b42b259b401.png?resizew=157)
(1)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70db40c42655327adee01caedfc9d50c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27ed8cad5482fe2742ef4aa65d1ddcb.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70db40c42655327adee01caedfc9d50c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2023-11-29更新
|
405次组卷
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2卷引用:江苏省扬州市扬州中学2024届高三下学期开学检测数学试题
10 . 如图,直三棱柱ABC-A1B1C1中,BA=BC=BB1=1,BA⊥BC
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/25/569dd342-e098-4f4e-9fb3-d055fc2e06a6.png?resizew=186)
(1)记平面
平面
,证明:
平面
;
(2)点Q是直线
上的点,若直线
与
所成角的余弦值为
,求线段
长.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/25/569dd342-e098-4f4e-9fb3-d055fc2e06a6.png?resizew=186)
(1)记平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/116aecda1a8df2a36a50941390a510a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6097e56f0e6cb49dfea1b5ba6805c61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23976db53f05b3d5d791c4d736a7184d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
(2)点Q是直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991a908f49f9deb228415dcb3d9248aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabe764f05300ac83c7d16b685d27af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
您最近一年使用:0次