名校
解题方法
1 . 如图,在长方体
中,
,
和
交于点E,F为AB的中点.
平面
;
(2)已知
与平面
所成角为
,求点A到平面CEF的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8745717601cd14b46c2298919b41b502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
您最近一年使用:0次
2024-01-05更新
|
443次组卷
|
5卷引用:宁夏石嘴山市平罗中学2024届高三上学期第四次月考数学(文)试题
宁夏石嘴山市平罗中学2024届高三上学期第四次月考数学(文)试题江西省景德镇市景德镇一中2024届高三上学期1月考试数学试题(已下线)专题8.9 空间角与空间距离大题专项训练-举一反三系列(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)(已下线)重难点专题15 空间中的五种距离问题-【帮课堂】(苏教版2019必修第二册)
2 . 如图,在四棱锥
中,底面
是边长为2的菱形,
,且
平面
,
,
,
分别是
,
的中点,
是
上一点,且
.
(1)求证:
平面
;
(2)若
,求直线
与平面
所成角的余弦值.
![](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/a23f01af749100e1888bba06268843db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae890f9e8b32aa53a54158f24f4a87bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da555a86cdae155dea2a093188989dfc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/1/d16b7ffb-a40f-468f-b7ae-e50de7ca5996.png?resizew=178)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debdc6632a4877e5131d3da25cda8b89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/970bd8c6012979f91c4b370fad352d47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,线段
是圆柱
的母线,
是圆柱下底面
的直径.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/27/cddc9e29-e80b-441e-bad9-84edc04eb170.png?resizew=133)
(1)弦
上是否存在点
,使得
∥平面
,请说明理由;
(2)若
,
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/27/cddc9e29-e80b-441e-bad9-84edc04eb170.png?resizew=133)
(1)弦
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c2e528bb8fc7c95fec7ecc510d04034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc1c04946340198af69170d4ebd4b42.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f97abea909791f73b84a07d3f15d8535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb01d2b57580731c8b807ac8cffc8ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
您最近一年使用:0次
名校
解题方法
4 . 已知四棱锥
中,底面ABCD为平行四边形,
底面ABCD,若
,
,E,F分别为
,
的重心.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/19/a7720b20-45ce-4f05-95dd-48d4c3c842cc.png?resizew=205)
(1)求证:
平面PBC;
(2)当
时,求平面PEF与平面PAD所成角的正切值.
![](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/0d6baf49925a5bcb359b542d45067c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/19/a7720b20-45ce-4f05-95dd-48d4c3c842cc.png?resizew=205)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2951b9f77413d5f062acb300b09de1f6.png)
您最近一年使用:0次
2023-04-16更新
|
808次组卷
|
5卷引用:宁夏平罗中学2023届高三第四次模拟数学(理)试题
名校
解题方法
5 . 如图,在三棱柱
中,
是边长为2的等边三角形,
,平面
平面
分别为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/c6445c5f-c5f9-49a1-bcb4-d7a94e49b79d.png?resizew=246)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
;
(2)若三棱柱
的体积为
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252143a7b900d33862f60b2536f6a8ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12fa54e80fc52de0701cddc9a4ed47e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ea285e96bf2e3b6406151bb694f10a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/c6445c5f-c5f9-49a1-bcb4-d7a94e49b79d.png?resizew=246)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)若三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
您最近一年使用:0次
2023-04-16更新
|
1645次组卷
|
4卷引用:宁夏银川市银川一中2024届高三上学期第五次月考数学(文)试题
宁夏银川市银川一中2024届高三上学期第五次月考数学(文)试题河南省商丘市部分学校2022-2023学年高中毕业班阶段性测试(六)文科数学试题第13章《立体几何初步》单元达标高分突破必刷卷(基础版)-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(苏教版2019必修第二册)(已下线)第四章 立体几何解题通法 专题二 体积法 微点1 体积法(一)【基础版】
名校
解题方法
6 . 《九章算术》卷第五《商功》中有记载:“刍甍者,下有袤有广,而上有袤无广.刍,草也,甍,屋盖也.”翻译为“底面有长有宽为矩形,顶部只有长没有宽为一条棱.刍甍字面意思为茅草屋顶,”现有“刍甍”如图所示,四边形EBCF为矩形,
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/1/a26267da-9876-43d1-8497-7ad7894634cd.png?resizew=255)
(1)若O是四边形EBCF对角线的交点,求证:
平面GCF;
(2)若
,且
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/337af9cda1547d80b130e2d7276fc305.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2868936b67397a7957f873a9956d396.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/1/a26267da-9876-43d1-8497-7ad7894634cd.png?resizew=255)
(1)若O是四边形EBCF对角线的交点,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a2f83ac39a73f4f01fb8068a0556fa8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce726bceb02452bb4e5ed6b00fa94e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5575930a695a591ae96e3f7d9dbb608e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc3bf74119692ac98eb24fcfa2a3f9f.png)
您最近一年使用:0次
2023-03-30更新
|
847次组卷
|
5卷引用:宁夏回族自治区银川市宁夏育才中学2023届高三第三次模拟数学(文)试题
名校
解题方法
7 . 如图,在直角梯形ABCD中,
,
,四边形CDEF为平行四边形,平面
平面ABCD,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/954e69aa-c4ad-4b09-a941-9e4a91deb1d0.png?resizew=175)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
平面ABE;
(2)若
,
,
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5a68a008a22d5a8cea5fe8dcf31e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ee81b6066188abee9d167b6c7f3f71.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/954e69aa-c4ad-4b09-a941-9e4a91deb1d0.png?resizew=175)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d37014607e7d8ded383597baae738bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e623b96c388d215c3ef28869a61f00e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd3df0e78cc51865a46aa0ac013bc44.png)
您最近一年使用:0次
2023-03-22更新
|
1432次组卷
|
8卷引用:宁夏银川市六盘山高级中学2023届高三三模数学(文)试题
宁夏银川市六盘山高级中学2023届高三三模数学(文)试题河南省2022-2023学年高三下学期核心模拟卷(中)文科数学(一)试题青海省西宁市大通回族土族自治县2023届高三第二次模拟考试文科数学试题青海省西宁市2023届高三二模数学(文科)试题四川省成都列五中学2022-2023 学年高三下学期阶段性考试(二)暨三诊模拟考试文科数学试题(已下线)专题06空间位置关系的判断与证明四川省成都市名校2022-2023学年高三下期4月定时训练文科数学试题(已下线)2024年全国高考名校名师联席命制数学(文)信息卷(十)
8 . 正方体
中,AC与BD交于点O,点E,F分别为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/21/95472ad1-e8d7-4568-bb71-dcd9604aae07.png?resizew=194)
(1)求证:平面
平面BEO;
(2)若正方体的棱长为2,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e86e3991200297ad172455e5ea93f5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/21/95472ad1-e8d7-4568-bb71-dcd9604aae07.png?resizew=194)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac9bbbb23bd5e1cbe61408bd632350f3.png)
(2)若正方体的棱长为2,求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e80318b27b799587e8771a6b6270dbd1.png)
您最近一年使用:0次
2023-03-21更新
|
531次组卷
|
4卷引用:宁夏回族自治区石嘴山市第三中学2023届高三第四次模拟考试数学(文)试题
宁夏回族自治区石嘴山市第三中学2023届高三第四次模拟考试数学(文)试题贵州省毕节市2023届高三诊断性考试(二)数学(文)试题(已下线)专题13 押全国卷(文科)第18题 立体几何(已下线)专题13立体几何(解答题)
解题方法
9 . 如图,圆锥SO的侧面展开图是半径为2的半圆,AB,CD为底面圆的两条直径,P为SB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/9/bd603ecf-06d1-4c47-88c1-9c941924ddbb.png?resizew=165)
(1)求证:
平面PCD;
(2)当
体积最大时,求S到平面PCD的距离.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/9/bd603ecf-06d1-4c47-88c1-9c941924ddbb.png?resizew=165)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9428c4a6a25d360a036aaf0a92e40988.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427be7dea704e748b1903d6aaebec9f9.png)
您最近一年使用:0次
名校
解题方法
10 . 如图,在直三棱柱
中,
,
是棱
的中点,
为线段
与
的交点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/1296b744-c1d9-462e-8b95-a0087f327566.png?resizew=163)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
平面
;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46d387c5e3c0a9d9c096e84907b21407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/1296b744-c1d9-462e-8b95-a0087f327566.png?resizew=163)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
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2022-12-16更新
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2卷引用:宁夏石嘴山市第三中学2024届高三上学期第二次月考数学(文)试题