解题方法
1 . 如图,正方体
的棱长为3,点
在棱
上,点
在棱
上,
在棱
上,且
,
是棱
上一点.
,
,
,
四点共面;
(2)若平面
平面
,求证:
为
的中点.
(3)求平面
与平面
所成二面角的余弦值.
![](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/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d8fd9dbd9c0967145625b394f8182f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e5ae0b183a311481b4c833959b068cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6069dc466eec75bbeb3d5c9b51cb3a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef5ea43614d815c3abb27a42dfb101b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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7日内更新
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2卷引用:海南省2020-2021学年高二下学期期末考试数学试题
名校
2 . 如图,,
为圆柱
的母线,
是底面圆
的直径,
,
分别是
,
的中点,
平面
.
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b78172568aac9805d2ea2d5f742bf80c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e78a23ef615a0815e2cf7b226c418dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b94e97d085cea077cb82a0b7d2f523e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d3f9e8e58175cc46453515621e69193.png)
您最近一年使用:0次
3 . 正方体ABCD﹣A1B1C1D1中,E是棱A1D1中点,F是棱AB中点,G是棱BC中点,作出过E,F,G的平面截得正方体的截面形状.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/15/30c19b30-b4e1-447b-9f49-c2d12cf201f2.png?resizew=167)
您最近一年使用:0次
名校
解题方法
4 . 如图,在直三棱柱
中,
为棱
上靠近
的三等分点,
为棱
的中点,点
在棱
上,且直线
平面
.
![](https://img.xkw.com/dksih/QBM/2022/8/23/3050868189208576/3053039154298880/STEM/4edb939b90ac48f9ab1be3f00fb58dc5.png?resizew=249)
(1)求
的长;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac13ff933d5ab9ba648d7299628a694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69fd379efd21837a27bdaf4e90b99367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9c33c356781f0f691d082ee8a32204.png)
![](https://img.xkw.com/dksih/QBM/2022/8/23/3050868189208576/3053039154298880/STEM/4edb939b90ac48f9ab1be3f00fb58dc5.png?resizew=249)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b676c6ffdb546ddb77e6740b20e3cdb.png)
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2022-08-26更新
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3卷引用:湖北省鄂南高级中学2021-2022学年高二上学期9月起点考试数学试题
解题方法
5 . 如图,平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
,
,
,
,
,直线
与
交于点
,且
,
,
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4cc2f3dcb248fc764614be3a9ddd25b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaccf1887c4b530fd86a2f0f199c6797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3da3fdf44b48a0d66b87441fc699cab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffd4fbbe51e32915593dc8bcf1a1e0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/774f29f3a042bdbe3f9f15401c25d98e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d5ba423355565d1888cf72f40e917d.png)
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2023-04-19更新
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1009次组卷
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3卷引用:6.4.2平面与平面平行的性质 课时练习2020-2021学年高一下学期数学北师大版(2019)必修第二册
6.4.2平面与平面平行的性质 课时练习2020-2021学年高一下学期数学北师大版(2019)必修第二册第六章 立体几何初步(单元基础检测卷)(已下线)第8.5.3讲 平面与平面平行-同步精讲精练宝典(人教A版2019必修第二册)
解题方法
6 . 已知平面
平面
,直线
平面
,且点
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60be170a52db82cf37b30db0cde26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23976db53f05b3d5d791c4d736a7184d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb0b6de90bb936cdb09629123100145d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30262f17d1e521b48d773da22ebf452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1754786a3367aca3da18ee3316e5b968.png)
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名校
解题方法
7 . 已知底面边长和斜高长均为2的正四棱锥被平行于底面的平面所截得的正棱台为
,且满足
.
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9dcbb4a05aa3b0cf780baa4489556e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b54387f870ae37f7951b253665d64f6.png)
(2)求棱台的体积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2022高三·全国·专题练习
解题方法
8 . 在三棱柱
中,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/81988561-a64c-4273-8ebd-d2b99c05565f.png?resizew=151)
(1)若
分别是
的中点,求证:平面
平面
.
(2)若点
分别是
上的点,且平面
平面
,试求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/81988561-a64c-4273-8ebd-d2b99c05565f.png?resizew=151)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c2d86d8daea5e652d99fe1c6bc3f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df99f9068028c7f6983e001f7c70c8e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/803c694330ef9eb2cb494f3ed6778287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66536b6d4dd18013c97f385c3224416.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0ae07505d28385b5ae7fa6769e6f91b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c152744e7eb9d9f86eaf937ed96a737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bf345b86a78e5d8eba3bde4bae43774.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae7f4612c548b1f72a964ddb291cd2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/424dd73a238dad799c9296e9ff829253.png)
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2022-09-14更新
|
1030次组卷
|
11卷引用:第10课时 课中 空间中平面与平面的平行
(已下线)第10课时 课中 空间中平面与平面的平行(已下线)考点47 直线与平面、平面与平面平行-备战2022年高考数学一轮复习考点帮(新高考地区专用)【学科网名师堂】(已下线)7.1 空间几何中的平行(精练)(已下线)第03讲 空间直线、平面的平行 (精讲)-2(已下线)第47讲 直线与平面、平面与平面平行(已下线)第八章立体几何初步章末题型大总结(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)8.5.3 平面与平面平行(1)-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(人教A版2019必修第二册)(已下线)期末复习06 空间几何线面、面面平行-期末专项复习4.4.1 平面与平面平行(已下线)专题6-3立体几何大题综合归类-1(已下线)8.5.3 平面与平面平行 (第1课时) 平面与平面平行的判定(分层作业)-【上好课】
名校
9 . 如图,矩形
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c707f0202ec1aa233e1eeacc7a4587d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e4201ad1d4e25974c60439c2a561c08.png)
,平面
与棱
交于点G.
;
(2)求直线
与平面
夹角的正弦值;
(3)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5d5f5199a80748d7a3afa1ac0c99135.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c707f0202ec1aa233e1eeacc7a4587d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e4201ad1d4e25974c60439c2a561c08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ccb204e61b8daace3f89787e8fdd39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa3254460ecbacecb3e57c5dce227f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df55452b4b5fcdcb71f713b736f8b9e1.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa3254460ecbacecb3e57c5dce227f4.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a06f9624936200b73a5b0ce0b5bdfad.png)
您最近一年使用:0次
2022-10-26更新
|
705次组卷
|
2卷引用:北京市丰台区第十二中学2021-2022学年高二上学期期中数学试题
名校
10 . 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
|
874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