名校
解题方法
1 . 如图,在菱形ABCD中,
,点P是菱形ABCD所在平面外一点,
,
平面ABCD.平面PCD与平面PAB交于直线l.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/8/6b567ceb-ab24-4c48-85d7-cabe3d1fe722.png?resizew=131)
(1)求证:
平面ABCD;
(2)求点D到平面PAB的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3ebf9b8d9cd253e2be1814b6c488a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/8/6b567ceb-ab24-4c48-85d7-cabe3d1fe722.png?resizew=131)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23976db53f05b3d5d791c4d736a7184d.png)
(2)求点D到平面PAB的距离.
您最近一年使用:0次
2023-10-20更新
|
462次组卷
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3卷引用:上海市浦东新区上海市实验学校2024届高三上学期第三次月考数学试题
名校
解题方法
2 . 如图,在四棱锥
中,底面
是矩形,其中
,
,
底面
,
,
为
的中点,
为
的中点.
(1)证明:直线
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a5faf3cbb633fc4294c8ce703c64c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4317430d5a2b61d9a2a88b73e7d7ad39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9774f83067ed956a551bc41adcce0469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/6/68e9d843-fc85-4db1-837e-3af70dd6a431.png?resizew=144)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3201d3796ed9a29338aac25245a7c8e2.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3201d3796ed9a29338aac25245a7c8e2.png)
您最近一年使用:0次
2023-10-18更新
|
822次组卷
|
2卷引用:上海市进才中学2024届高三上学期10月月考数学试题
22-23高二下·上海浦东新·阶段练习
名校
解题方法
3 . 如图,三棱柱
的底面是边长为2的正三角形,侧棱
垂直于底面ABC,
,D是CB延长线上一点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/19/ba990b48-df50-4bbf-a1d8-6ad4ef5e2501.png?resizew=198)
(1)证明:直线
平面
;
(2)求二面角
的大小;
(3)直线
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/295640e886a3a29c5159a93fa287ee68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78002bca853929365a3f58082f3e7637.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/19/ba990b48-df50-4bbf-a1d8-6ad4ef5e2501.png?resizew=198)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb689000fa7a3b425be3196d8b0f32af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5888bec948373f3854258ad80171073d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c34f1c900792fb9fadded8982d6d042.png)
(3)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5888bec948373f3854258ad80171073d.png)
您最近一年使用:0次
名校
4 . 如图,在正三棱柱
中,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/d35717d7-88cb-4dfd-a964-4d6986d9d191.png?resizew=153)
(1)证明:
平面
;
(2)求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16cfb38323095090b0fe5eee70b24210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/d35717d7-88cb-4dfd-a964-4d6986d9d191.png?resizew=153)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec47f6d6cb1eeefbb466e4fe71fd568c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
您最近一年使用:0次
2023-02-21更新
|
861次组卷
|
4卷引用:上海师范大学附属中学2024届高三上学期9月月考数学试题
21-22高二上·上海浦东新·阶段练习
名校
解题方法
5 . (1)请用符号语言叙述直线与平面平行的判定定理;
(2)把(1)中的定理用反证法证明;
(3)如图,在正方体
中,点N在
上,点M在
,且
,求证:
平面
(用(1)中所写定理证明)
(2)把(1)中的定理用反证法证明;
(3)如图,在正方体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d88aaea5b185ca38fe1026869c7a5fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/20/2851ac28-aed5-411b-976e-90e5e85eaf37.png?resizew=164)
您最近一年使用:0次
2023-10-20更新
|
254次组卷
|
6卷引用:上海市华东师范大学第二附属中学2021-2022学年高二上学期9月质量调研数学试题
(已下线)上海市华东师范大学第二附属中学2021-2022学年高二上学期9月质量调研数学试题(已下线)上海市华东师范大学第二附属中学2021-2022学年高二上学期10月月考数学试题上海市敬业中学2023-2024学年高二上学期10月月考数学试题(已下线)10.3 直线与平面平行的判定定理(第1课时)(已下线)第04讲线线、线面、面面平行的判定与性质(核心考点讲与练)(3)(已下线)第一章 点线面位置关系 专题一 空间平行关系的判定与证明 微点3 直线与平面平行的判定与证明【基础版】
名校
6 . 如图,在四棱锥
中,底面
是矩形,
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/21/c82d7471-da04-480f-95db-e407c0d67d6d.png?resizew=164)
(1)若点
,
分别为
,
的中点,求证:直线
平面
;
(2)求直线
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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f30be4069b0a5a105bb85e884165569.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/21/c82d7471-da04-480f-95db-e407c0d67d6d.png?resizew=164)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2023-11-21更新
|
615次组卷
|
2卷引用:上海市浦东新区建平中学2024届高三上学期11月质量检测数学试题
名校
7 . 如图,在四棱锥
中,
面
,
,
,点
分别为
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/71654a21-d300-4c81-a8f2-9f2d03018911.png?resizew=176)
(1)证明:直线
平面
;
(2)求二面角
的余弦值.
![](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/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4762d59261265112fef9ac74d5bb9a36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c3ca1c27bdc0102bf2c6b306ddd1d95.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/71654a21-d300-4c81-a8f2-9f2d03018911.png?resizew=176)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc6bc85b019e9d158ca1d92feed796e.png)
您最近一年使用:0次
2023-01-15更新
|
1365次组卷
|
11卷引用:上海市华东师范大学第二附属中学2023届高三下学期2月月考数学试题
(已下线)上海市华东师范大学第二附属中学2023届高三下学期2月月考数学试题(已下线)上海市华东师范大学第二附属中学2023届高三最后一模数学试题上海市嘉定区第一中学2024届高三上学期10月月考数学试题陕西省兴平市南郊高级中学2023-2024学年高二上学期第三次质量检测数学试题四川省达州市2022-2023学年高二上学期期末监测数学(理科)试题(已下线)第8章 立体几何初步 重难点归纳总结-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)专题2 求二面角的夹角(1)(已下线)8.6.3 平面与平面垂直(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)专题8.16 空间角大题专项训练(30道)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)上海市同济大学第二附属中学2024届高三上学期期中数学试题海南省琼海市海桂中学2023-2024学年高二上学期期中考试数学试题(B卷)
8 . 如图,在长方体
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9223d0a3517bd3f28386152fe0e8ef8a.png)
分别为
的中点.点
在平面
内,若直线
平面
,则线段
长度的最小值是______ ・
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9223d0a3517bd3f28386152fe0e8ef8a.png)
分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572c2f57dce9bb7458f71d84f3c6a725.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff55f4780bb3fb376c9a04dbfbb1d989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c798204bbe306b3efd5bc9eae594c171.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/5576e745-6e26-4ada-888e-cb3de2861a4b.png?resizew=164)
您最近一年使用:0次
2022-11-21更新
|
886次组卷
|
13卷引用:上海市洋泾中学2022-2023学年高二上学期10月质量检测数学试题
上海市洋泾中学2022-2023学年高二上学期10月质量检测数学试题上海市进才中学2022-2023学年高二上学期10月月考数学试题上海市大同中学2022-2023学年高二上学期10月月考数学试题上海市市北中学2023-2024学年高二上学期10月月考数学试题苏教版(2019) 必修第二册 过关斩将 第13章 13.2.4 平面与平面的位置关系 第1课时 两平面平行(已下线)上海高二上学期期中【常考60题考点专练】(2)(已下线)数学(上海A卷)上海市嘉定区第一中学2021-2022学年高二上学期期中数学试题(已下线)8.5 空间直线、平面的平行(精练)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)8.5.3 平面与平面平行(分层作业)-【上好课】2022-2023学年高一数学同步备课系列(人教A版2019必修第二册)(已下线)6.4.2平面与平面平行(课件+练习)2023版 湘教版(2019) 必修第二册 过关斩将 第4章 4.4 平面与平面的位置关系 4.4.1 平面与平面平行上海市格致中学2023-2024学年高二上学期期中数学试题
解题方法
9 . 如图,在四棱锥
,底面
是正方形,侧面
底面
,且
,若
、
分别为
、
的中点.求证:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/facb2261-cd7d-4e3d-aac2-ddce94e97cdb.png?resizew=219)
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
;
(2)
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6be2b61f4a38e2ee2c1a01e00b3ae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2c4cc37d6ba218107c9c5d820740fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18037eb1473bf29cbeadabf51fca022f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252053b853152bd294a8315debd00b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655b6a742dbacdab5aaa298007663dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/facb2261-cd7d-4e3d-aac2-ddce94e97cdb.png?resizew=219)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92dc7c262bba52d1b97c17c6d07e9d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
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解题方法
10 . 在正方体
中,M,N,P分别为
,AD,
的中点,棱长为1.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/14/e146b5d5-617e-49a1-9ba0-cc78811c0c1c.png?resizew=176)
(1)求证:
平面
;
(2)过M,N,P三点作正方体的截面,画出截面(保留作图痕迹),并计算截面的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1adfcfa3dbc655af0f42d8773eb7710f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb16f7dbc4b9993c4efa0764df1d8ca.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/14/e146b5d5-617e-49a1-9ba0-cc78811c0c1c.png?resizew=176)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3123da0313d458c833e82aaa234b9117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d80ed37728f5933020ccb894541e857.png)
(2)过M,N,P三点作正方体的截面,画出截面(保留作图痕迹),并计算截面的周长.
您最近一年使用:0次
2022-10-11更新
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552次组卷
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3卷引用:上海市洋泾中学2022-2023学年高二上学期10月质量检测数学试题