解题方法
1 . 如图,正方形
与梯形
所在平面互相垂直,已知
,
,
.
(1)求证:
平面
.
(2)线段
上是否存在点M,使平面
平面
?若存在,求出
的值;若不存在,请说明理由.
![](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/5408641691fd27f6dd8cf0ab2043ad4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ae5f8381ffcce4281a0ca817b82a41.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/21/93667f7c-593c-418d-b3c2-16a4c960decb.png?resizew=160)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2f2eae3483395cc6aca5160c64f83eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7084fef1f20c7af36659c1faa643ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cada49bc5cf1cf8615eaf91863d18535.png)
您最近一年使用:0次
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解题方法
2 . 如图,在四面体
中,
是
中点,
是
中点.在线段
上存在一点
,使得
平面
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9abe6e8d1f4f1e8bdc46ddbae0cd789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/412b394ab196e93ba49f115d0a8cacd6.png)
A.1 | B.2 | C.3 | D.![]() |
您最近一年使用:0次
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3 . 如图,在三棱柱
中,
平面
,点
,
分别在棱
和棱
上,且
为棱
中点.
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ef601ca1f9c4c031adab4ffed297f0.png)
平面
;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8bfe2553e852df73185d017c0a62fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f91f0d1a4e368147e3783c9374461b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d8379e02133be85a72747674b14f86f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/20/bcd417f3-2372-40f6-9065-4f82b3115e7e.png?resizew=150)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ef601ca1f9c4c031adab4ffed297f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0278f9809e118b80c9946d9b9ae40c83.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bffd657e48b15b9b54a55817e2c26b22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/024d58baa25d2565912a9e6e3a06dbe2.png)
您最近一年使用:0次
2023-10-18更新
|
626次组卷
|
2卷引用:辽宁省六校协作体2023-2024学年高二上学期10月联考数学试题
名校
解题方法
4 . 直四棱柱
中,
,
,
,
,
.
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
平面
;
(2)若四棱柱
的体积为36,求二面角
的大小.(结果要求用反正切表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee8ef58be8708144272538ee427fb92c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49437f474e5805688dff21ded2d1fd7c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/6/55feb31a-1a0a-41d2-9463-59ed9d1477b1.png?resizew=156)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b54387f870ae37f7951b253665d64f6.png)
(2)若四棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab6ad3d3e3064fa417a02dba02dbf04.png)
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5 . 如图,
平面
,
,
,
,
,
.
(1)求证:
平面ADE;
(2)求直线
与平面
所成角的正弦值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e952f7b05d06917128bfecb64fe3cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d262480ffb55b7617f44b63f130c154a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411d1139c919736044af6379743b3d5c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/19/969c133f-90d5-4249-b502-93945700d5df.png?resizew=157)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8ccd4181f956f6e0140bf0ab8f0716.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
您最近一年使用:0次
2023-10-17更新
|
492次组卷
|
3卷引用:黑龙江省大庆第一中学2023-2024学年高二上学期第二次验收考试数学试题
2019高一上·全国·专题练习
名校
解题方法
6 . 已知
为
所在平面外一点,平面
平面
,且
交线段
,
,
于点
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60be170a52db82cf37b30db0cde26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d100e7830d2e9d27bdccb181c79b65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c7c4947f84a1e1c1ee994a8cc38ac3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf4f8909d3fe0b2b0327882d55610a27.png)
A.2:3 | B.2:5 | C.4:9 | D.4:25 |
您最近一年使用:0次
2023-10-17更新
|
507次组卷
|
9卷引用:北京理工大学附属中学2023-2024学年高二上学期10月练习数学试题
北京理工大学附属中学2023-2024学年高二上学期10月练习数学试题江西省南昌市湾里管理局第一中学等六校2021-2022学年高二下学期期中联考数学(文)试题(已下线)2019年12月27日《每日一题》-直线、平面平行的判定及其性质专题6.3 空间中的平行关系-2021-2022学年高一数学北师大版2019必修第二册(已下线)第七章 立体几何与空间向量 第三节?第二课时直线,平面平行的判定与性质(A素养养成卷)(已下线)第09讲 空间的平行关系-【寒假预科讲义】(人教A版2019必修第二册)(已下线)第08讲 8.5.1 直线与直线平行-【帮课堂】(人教A版2019必修第二册)(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2 空间直线平行的判定与证明综合训练【基础版】(已下线)8.5.3 平面与平面平行-同步精品课堂(人教A版2019必修第二册)
名校
解题方法
7 . 在棱长为2的正方体
中,点M是对角线
上的点(点M与A、
不重合),则下列结论正确的是______________ .(请填写序号)
①存在点M,使得平面
平面
;
②存在点M,使得
平面
;
③若
的面积为S,则
;
④若
、
分别是
在平面
与平面
的正投影的面积,则存在点M,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/8/ff785f15-c66b-43ee-bd82-a02f45c1820f.png?resizew=157)
①存在点M,使得平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dba49eb8ddd4dd38c1f994ccec93430e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
②存在点M,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0457394ce4f2dc8d940c565c94dcf557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0a582c36d62d83c16425b2f54b4354.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce447afe4b0bb57a844b2c103b55fc71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42910d271417cc2435d0affa6c85afd5.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce447afe4b0bb57a844b2c103b55fc71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31dd78e9156dcf6db93f6cbcc5b43b14.png)
您最近一年使用:0次
8 . 如图,在三棱锥
中,
两两互相垂直,
分别为棱
的中点,
是线段
的中点,且
(1)求证:
平面
.
(2)在棱
上是否存在一点
,使得直线
与平面
所成的角为
,若存在,求线段
的长;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa2462f1dbb5a91c22f61a73993ace9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3b9a4cf42189f9ef786b3c549ecd93e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55928df632fc6f2b88a44afe37e5a4e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e27d4e37cdd620a718e5dd741f823b81.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/19/1c741a53-88b4-4b65-bf1d-a99a0a2ce728.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9d2abf13c2842f58654abf73c6b4ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
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9 . 如图,
,O分别是圆柱上、下底面圆的圆心,该圆柱的轴截面是边长为2的正方形ABCD,P,Q分别是其上、下底面圆周上的动点,已知P,Q位于轴截面ABCD的异侧,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/2/99f4e9b5-0314-479a-9b68-3bb5c27b0d29.png?resizew=130)
(1)当A,P,
,Q四点共面时,求
;
(2)当
时,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37389700fb7678d1d1ec0b5ba13e16b4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/2/99f4e9b5-0314-479a-9b68-3bb5c27b0d29.png?resizew=130)
(1)当A,P,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/905dd10639c9fef5ef8d66a124756140.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d5e1af15b01646e12b8ec729dfd0da2.png)
您最近一年使用:0次
2023-10-14更新
|
404次组卷
|
2卷引用:辽宁省沈阳市第一二〇中学2023-2024学年高二上学期第二次质量监测数学试题
10 . 已知正方体
,点P满足
,
,
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab006ce970f48340a79281d523783aa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee72261f6901e62dfd0ffe547406544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e2e01346f60857ff635bb766802e57.png)
A.三棱倠![]() |
B.当![]() ![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() |
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