名校
1 . 如图,在四棱锥
中,底面
正方形,平面
底面
,平面
底面
,
,
分别是
的中点,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/16/dff7d99f-8875-4564-93ce-c46cc758ab86.png?resizew=173)
(1)证明:
平面
;
(2)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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36dc88c2054948a03e74d57b10d3a482.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e658d7985a600629fdf01517fc55c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67576cc7b83ee93cfd15154bb2a00c5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/16/dff7d99f-8875-4564-93ce-c46cc758ab86.png?resizew=173)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96b8c2721ada247b03f41f328539b301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
您最近一年使用:0次
2022-09-16更新
|
1100次组卷
|
4卷引用:广东省广州市天河外国语学校2022-2023学年高二上学期期中数学试题
名校
2 . 如图,在多面体
中,平面
平面
.四边形
为正方形,四边形
为梯形,且
,
是边长为1的等边三角形,
为线段
三等分点(靠近点
),
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/28/7678c3e5-bc5e-4acc-ba99-f66e71160243.png?resizew=237)
(1)求证:
;
(2)求直线
与平面
所成角的正弦值;
(3)线段
上是否存在点
,使得直线
平面
?若存在,求
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866a6cb2f0ef738f62fa9fa372c0819b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d16a4959a99193a52d6fa8648cb2eb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a28be4d5a16cf245f6fa7c4088fee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da9dcf6c319174c9ea2b1ceaed1649a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f02795ff1af51fb0672800ceb02e7893.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/28/7678c3e5-bc5e-4acc-ba99-f66e71160243.png?resizew=237)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc553932ce81b2c940b34b28d80c8146.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(3)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe9eeee83b4b7c6ceac7828ff534ce15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a20ea69475dcf57a5ff18c13eceaaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff65109fbe7d397800f32b47cf38a22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a459b45690bb921bbae09065b3df9f1f.png)
您最近一年使用:0次
2022-10-26更新
|
873次组卷
|
2卷引用:福建省泉州第一中学2021-2022学年高二上学期期中考试数学试题
名校
解题方法
3 . 如图,在三棱柱
中,四边形
为菱形,
,平面
平面
﹐Q在线段AC上移动,P为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/c4b7a15c-4f94-4d35-a9ba-ea41b93ccf29.png?resizew=207)
(1)若H为BQ中点,延长AH交BC于D,求证:
平面
﹔
(2)若二面角
的平面角的余弦值为
,求点P到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f0d0e78101fef36a75b70ac7e7cf5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09e20ab4f192002c79ccb7ff7f9d63ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e2385ec6765cff01b2d00664d4aad7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/c4b7a15c-4f94-4d35-a9ba-ea41b93ccf29.png?resizew=207)
(1)若H为BQ中点,延长AH交BC于D,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5edfe97aeab0cf16b40fa9d2e15f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04ffba8658b0023316117e1536cbf806.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39eefa58485e43a86a1931a2aa7222a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5ec70bc9d4f8f5df312e2f09ee3bcb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fed1f54c1b008a633326db4f20288c5.png)
您最近一年使用:0次
2022-05-27更新
|
790次组卷
|
12卷引用:辽宁省大连市大连育明高级中学2022-2023学年高二上学期期中数学试题
辽宁省大连市大连育明高级中学2022-2023学年高二上学期期中数学试题河北省衡水中学2018届高三考前适应性训练6月1日第3天数学(理)试题人教A版(2019) 选择性必修第一册 必杀技 第一章 空间向量与立体几何 素养检测人教B版(2019) 选择性必修第一册 必杀技 第一章 空间向量与立体几何 素养检测北师大版(2019) 选修第一册 必杀技 第三章 素养检测湖南省邵阳市第二中学2021-2022学年高二下学期入学考试数学试题辽宁省沈阳市2022届高三三模考试数学试题章节综合测试-空间向量与立体几何山东省东营市广饶县第一中学2022-2023学年高三上学期12月月考数学试题北师大版(2019) 选修第一册 章末检测卷(三) 空间向量与立体几何(已下线)第一章 空间向量与立体几何(单元提升卷)-2022-2023学年高二数学考试满分全攻略(人教A版2019选择性必修第一册)四川省宜宾市叙州区第二中学校2024届高三一模数学(理)试题
21-22高一下·浙江·期中
4 . 已知三棱锥
中,△ABC,△ACD都是等边三角形,
,E,F分别为棱AB,棱BD的中点,G是△BCE的重心.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/30/4c768d18-52ee-428a-958c-36eeb689cbf2.png?resizew=196)
(1)求异面直线CE与BD所成角的余弦值;
(2)求证:FG
平面ADC.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b94651d11df3a469d7ac72e6ac74c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/30/4c768d18-52ee-428a-958c-36eeb689cbf2.png?resizew=196)
(1)求异面直线CE与BD所成角的余弦值;
(2)求证:FG
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
您最近一年使用:0次
名校
5 . 如图所示,正方形
与梯形
所在的平面互相垂直,已知
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/662cf6ff-1732-4238-953f-0b4a263eeba5.png?resizew=192)
(1)求证:
平面
;
(2)求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8c9773e77146de880f1204dd9ef4593.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/662cf6ff-1732-4238-953f-0b4a263eeba5.png?resizew=192)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d32e76582bf550593fdef53e081225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
您最近一年使用:0次
2022-04-10更新
|
523次组卷
|
2卷引用:江苏省盐城市响水县第二中学2021-2022学年高二(11-18班)下学期期中数学试题
名校
6 . 如图,三棱柱
中侧棱与底面垂直,且AB=AC=2,AA1=4,AB⊥AC,M,N,P,D分别为CC1,BC,AB,
的中点.
(2)求平面PMN与平面ACC1A1所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9d2462e6dbd321cf3abae25a56adf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
(2)求平面PMN与平面ACC1A1所成锐二面角的余弦值.
您最近一年使用:0次
7 . 已知正方体ABCD−A1B1C1D1,O1为底面A1B1C1D1的中心.求证:
![](https://img.xkw.com/dksih/QBM/2022/5/9/2975686414393344/2976644283678720/STEM/322a5e8b-5fb8-41b9-b25e-4d48f2cfa846.png?resizew=195)
(1)平面AB1D1//平面C1BD;
(2)求直线D1A与BA1所成角.
![](https://img.xkw.com/dksih/QBM/2022/5/9/2975686414393344/2976644283678720/STEM/322a5e8b-5fb8-41b9-b25e-4d48f2cfa846.png?resizew=195)
(1)平面AB1D1//平面C1BD;
(2)求直线D1A与BA1所成角.
您最近一年使用:0次
解题方法
8 . 如图所示,正方形ADEF与梯形ABCD所在的平面互相垂直,已知
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/73e79a0f-8581-4fa1-a9e6-d307229998c3.png?resizew=215)
(1)求证:
平面
;
(2)连接
,求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffda707068a4a1778e79da6f20fb86d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/73e79a0f-8581-4fa1-a9e6-d307229998c3.png?resizew=215)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8ccd4181f956f6e0140bf0ab8f0716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
您最近一年使用:0次
2022-05-07更新
|
596次组卷
|
3卷引用:四川省成都市郫都区2021-2022学年高二下学期期中考试文科数学试题
解题方法
9 . 两个全等的正方形ABCD和ABEF所在平面相交于AB,
,
,且
,过M作
于H,求证:
![](https://img.xkw.com/dksih/QBM/2022/5/26/2987791805448192/2996112877002752/STEM/c75dbbb611b34434992d761b795c03eb.png?resizew=250)
(1)平面
平面BCE;
(2)
平面BCE.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e44a83de5184b7564ee4081a103f3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08dcbd87943e47ced0915da7f1005e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed2866bff71c094e32c1320690fff746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cbee40875112b88b7adcdcb297220f1.png)
![](https://img.xkw.com/dksih/QBM/2022/5/26/2987791805448192/2996112877002752/STEM/c75dbbb611b34434992d761b795c03eb.png?resizew=250)
(1)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02a094f09aa0326b8ef73b400d0d8e7.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
您最近一年使用:0次
10 . 如图,在长方体
中,
,
分别是线段
,
的中点.
平面
;
(2)若
,直线
与
所成角的余弦值是
,求四面体
的体积.
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a407b262c22419f73396170ecdc849.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/635a764c14e95e53a7a160d84706a449.png)
您最近一年使用:0次
2022-07-10更新
|
622次组卷
|
6卷引用:北京市第八十中学2023-2024学年高一下学期期中考试数学试题
北京市第八十中学2023-2024学年高一下学期期中考试数学试题湖南省五市十校教研教改共同体2021-2022学年高一下学期期末数学试题安徽省宣城市三校2022-2023学年高二上学期期初联考数学试题湖北省黄冈市黄州中学(黄冈外校)2022-2023学年高一下学期第七次阶段性测试数学试题福建省泉州第一中学2022-2023学年高二上学期暑假返校数学试题(已下线)8.5.3 平面与平面平行(第2课时) 平面与平面平行的性质(分层作业)-【上好课】