名校
解题方法
1 . 如图,在四棱锥
中,
,
,
,平面
平面ABCD.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/11/d3fcbb62-66d4-44cb-a135-eea80c3adfc1.png?resizew=169)
(1)证明:
平面PDC.
(2)若E是棱PA的中点,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
平面PCD,求点D到平面PAB的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25267f04873339a85a74c29e77ec2fc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0717c99cf54077d805c71254fa3230d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77eef0eaf87646c1692bdae799d194d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/11/d3fcbb62-66d4-44cb-a135-eea80c3adfc1.png?resizew=169)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95475bfc06e884754eb4a455c3f434e.png)
(2)若E是棱PA的中点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
您最近一年使用:0次
2022-07-05更新
|
1198次组卷
|
12卷引用:云南省楚雄州2021-2022学年高一下学期期末教育学业质量监测数学试题
云南省楚雄州2021-2022学年高一下学期期末教育学业质量监测数学试题河南省南阳地区2021-2022学年高一下学期期终摸底考试数学试题湖南省衡阳市部分校2021-2022学年高一下学期期末数学试题河北省邢台市2021-2022学年高一下学期期末数学试题广西贵港市2021-2022学年高一下学期期末教学质量监测数学试题吉林省白山市2021-2022学年高一下学期期末数学试题河北省承德市2021-2022学年高一下学期期末数学试题内蒙古自治区巴彦淖尔市2021-2022学年高一下学期期末数学试题广东省清远市2021-2022学年高一下学期期末数学试题贵州省遵义市道真仡佬族苗族自治县民族高级中学2022-2023学年高二上学期第一次月考数学试题江西省上高二中2022-2023学年高二上学期8月数学试题广东省连南瑶族自治县民族高级中学2022-2023学年高一下学期期中数学试题
解题方法
2 . 如图,在平面五边形
中,
为正三角形,
,
且
.将
沿
翻折成如图所示的四棱锥
,使得
.
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/18/9cdc4c3a-2016-4285-9513-7cdf8a81187b.png?resizew=445)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632917e61f4208959686d118c7f19231.png)
平面
;
(2)若
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1e3a43d0fa18f6c0888ba804d5b329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dceb5cc71fc50f20649f6b9535fd914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b377f22aafd3742ad860f77abaacef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae78aadc0434867ed7fd781574be9f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f82a30d6b232dc4d8f35d2d6e0e0f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/18/9cdc4c3a-2016-4285-9513-7cdf8a81187b.png?resizew=445)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632917e61f4208959686d118c7f19231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fccf15cd545019eb5d7fed1b4be1899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a681d311a864d38cf306a0c137cbcca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
2022-06-01更新
|
949次组卷
|
4卷引用:云南省普洱市2021-2022学年高二下学期期末考试数学试题
云南省普洱市2021-2022学年高二下学期期末考试数学试题山东省烟台市2022届高三三模数学试题(已下线)专题24 立体几何解答题最全归纳总结-1福建省泉州科技中学2022-2023学年高二上学期期中考试数学试题
名校
3 . 如图所示,直三棱柱
的所有棱长均相等,点D为
的中点,点E为
的中点.
![](https://img.xkw.com/dksih/QBM/2022/3/30/2947492456726528/2948197200707584/STEM/9b5f946b-1299-44bd-ab8a-b2216485d728.png?resizew=139)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
平面
;
(2)若三棱锥
的体积为
,求该三棱柱的外接球表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/2022/3/30/2947492456726528/2948197200707584/STEM/9b5f946b-1299-44bd-ab8a-b2216485d728.png?resizew=139)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
(2)若三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49c2bd5eaf71f8866c0979fa299df50d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a8b76e36783a69d14ec54af82c7df0.png)
您最近一年使用:0次
4 . 如图在四棱锥
中,底面
是边长为
的正方形,侧面
底面
,且
,设
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/2022/8/12/3042984151416832/3044289823014912/STEM/5c78d24c0c6b4f8daaf94acc86191ccd.png?resizew=264)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
;
(2)求直线
与平面
所成角的大小.
![](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/0a6936d370d6a238a608ca56f87198de.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/a1e030853e53547cc35df6ee1e033beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0ae9e915d670edaa52d9ad9f3f071a5.png)
![](https://img.xkw.com/dksih/QBM/2022/8/12/3042984151416832/3044289823014912/STEM/5c78d24c0c6b4f8daaf94acc86191ccd.png?resizew=264)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
解题方法
5 . 如图,P是四边形ABCD所在平面外的一点,四边形ABCD是
的菱形,
,平面PAD垂直于底面ABCD,G为AD边的中点. 求证:
![](https://img.xkw.com/dksih/QBM/2022/5/14/2979268881956864/2979747023134720/STEM/a597e7831c9a468f89b24bb9cad102b2.png?resizew=219)
(1)
平面PAD;
(2)若
,求多面体PABCD的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://img.xkw.com/dksih/QBM/2022/5/14/2979268881956864/2979747023134720/STEM/a597e7831c9a468f89b24bb9cad102b2.png?resizew=219)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf65b8884909d735d575efe81a2d2ad.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c0cf7a89ea148e0481a56f127297bb2.png)
您最近一年使用:0次
名校
解题方法
6 . 如图,在四棱锥
中,底面
是边长为2的菱形,
,
,E为AP的中点,
为等边三角形.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/3f1cc665-0981-4c8a-9f30-7c07ada6ec02.png?resizew=142)
(1)求证:
;
(2)在棱
上是否存在一点F,使
平面PBF,若存在,求点F到平面PBD的距离;若不存在,请说明理由.
![](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/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d390782b8ea7016628ee68403dcbfbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acee03d4bb4667b6c345221b6c9b0fa4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/3f1cc665-0981-4c8a-9f30-7c07ada6ec02.png?resizew=142)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb5d56d8170b764b80a672cd6c861921.png)
(2)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
您最近一年使用:0次
名校
7 . 如图,在三棱柱
中,已知
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/5bf5dca2-7345-4dd0-a113-cc7a8942fcfb.png?resizew=157)
(1)证明:平面
平面
;
(2)求二面角
的余弦值.
(注:本小题用空间直角坐标系作答,不给分 )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883fc5e3faf39829d60804b59deb1730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecb98a9240ab95180c6d1a2715e000d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a9f99fb3252a4b3b7a62e8a675ddce9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/5bf5dca2-7345-4dd0-a113-cc7a8942fcfb.png?resizew=157)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a2e10a5aebe40a9018d5ee3ade7af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10af6bf6d158e2d997b7bba250483b16.png)
(注:本小题用空间直角坐标系作答,
您最近一年使用:0次
2022-05-02更新
|
1459次组卷
|
4卷引用:云南省师大附中2021-2022学年高一下学期期中数学试题
云南省师大附中2021-2022学年高一下学期期中数学试题山西省太原市第五中学校2021-2022学年高一下学期5月阶段性检测数学试题福建省连城县第一中学2021-2022学年高一下学期月考(二)数学试题(已下线)专题09 立体几何中的角度、距离、体积问题-2021-2022学年高一数学下学期期末必考题型归纳及过关测试(人教A版2019)
8 . 如图,在四棱锥
中,底面
为菱形,
平面
,
,
为
的中点,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/5ee357dc-bbd0-4e87-b8ee-fe8c94a68ca5.png?resizew=168)
(1)求证:平面
平面
;
(2)若
,求点
到平面
的距离.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.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/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/5ee357dc-bbd0-4e87-b8ee-fe8c94a68ca5.png?resizew=168)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6501f1c913a4ef64957a2f01ab5baa15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
您最近一年使用:0次
2022-03-18更新
|
687次组卷
|
2卷引用:云南省普洱市2022届高三上学期期末统测数学(文)试题
9 . 如图,在四棱锥P-ABCD中,底面ABCD为平行四边形,E、F、G分别是棱AB、AP、PD的中点.
![](https://img.xkw.com/dksih/QBM/2022/5/9/2975774806204416/2976980659650560/STEM/0f4a35e0-ebef-4c25-8738-ff2d77922e2d.png?resizew=256)
(1)证明:
平面EFG;
(2)若
,
,求点C到平面EFG的距离.
![](https://img.xkw.com/dksih/QBM/2022/5/9/2975774806204416/2976980659650560/STEM/0f4a35e0-ebef-4c25-8738-ff2d77922e2d.png?resizew=256)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2597b5554284e275367c25529c6750f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cccb623839e5e6efb31056b83401763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32061e4f6ae667ddd700299a681d4240.png)
您最近一年使用:0次
2022-05-11更新
|
995次组卷
|
4卷引用:云南省昆明市2022届高三“三诊一模“高考模拟数学(文)试题
云南省昆明市2022届高三“三诊一模“高考模拟数学(文)试题(已下线)期末押题预测卷03-2021-2022学年高一数学下学期期末必考题型归纳及过关测试(人教A版2019)内蒙古呼和浩特市2023届高三第一次质量数据监测文科数学试题安徽省合肥市第七中学2022-2023学年高一下学期第二次单元检测(月考)数学试题
10 . 图甲是由直角梯形ABCD和等边三角形CDE组成的一个平面图形,其中
,
,
,将
沿CD折起使点E到达点P的位置(如图乙),在四棱锥
中,若
.
![](https://img.xkw.com/dksih/QBM/2022/4/6/2952461430677504/2953528282062848/STEM/0fd2c03d977941d6bdd0c3c54d0587df.png?resizew=398)
(1)证明:平面
平面ABCD;
(2)若平面PCD与平面PAB的交线为
,求
与平面ABCD的交点到平面PAD的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d730ae4307db56b47849c3a19dedfb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/727592aa1cb96156a7f572137ae50393.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecbb2dce15f3d0fe839688575d2a8ff8.png)
![](https://img.xkw.com/dksih/QBM/2022/4/6/2952461430677504/2953528282062848/STEM/0fd2c03d977941d6bdd0c3c54d0587df.png?resizew=398)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
(2)若平面PCD与平面PAB的交线为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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