名校
解题方法
1 . 在正方体
中,点
、
、
分别为棱
、
、
的中点,给出下列四个结论:①
;②
平面
;③异面直线
,
所成角的大小为
;④
平面
.其中所有正确结论的序号为( )
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d435974639ea2850bb5c21efe64b123b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd597851c0db4e4de4769e10e09383b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26d8a9d64ad3c8cba28840b41ed7837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
A.①② | B.②③ | C.①②③ | D.①②④ |
您最近一年使用:0次
2020-05-28更新
|
618次组卷
|
2卷引用:青海省海南州中学、海南州贵德中学2021-2022学年高二上学期期中考试数学(理)试题
名校
2 . 如图,在正方体
,点
在线段
上运动,则下列判断正确的是( )
![](https://img.xkw.com/dksih/QBM/2020/5/4/2455698308620288/2456116811620352/STEM/31b691fa-d95d-47c3-974f-82fd6592f860.png?resizew=238)
①平面
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
②
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
③异面直线
与
所成角的取值范围是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6216b5813de94fd730340d5c51e617e.png)
④三棱锥
的体积不变
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15f73038249a611568193c0bcc286fd7.png)
![](https://img.xkw.com/dksih/QBM/2020/5/4/2455698308620288/2456116811620352/STEM/31b691fa-d95d-47c3-974f-82fd6592f860.png?resizew=238)
①平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc954f644ebd405a780856f8c02cfe66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24579dca7ff1542ae019fc36110dddbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
③异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6216b5813de94fd730340d5c51e617e.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23e623d7180e345393af2fcde4e9c2b.png)
A.①② | B.①②④ | C.③④ | D.①④ |
您最近一年使用:0次
2020-05-05更新
|
1107次组卷
|
20卷引用:青海省湟川中学2020-2021学年高二下学期第一次月考数学(理)试题
青海省湟川中学2020-2021学年高二下学期第一次月考数学(理)试题宁夏银川三沙源上游学校2020-2021学年高一下学期第一次月考数学(理)试题湖南省衡阳市第八中学2020-2021学年高一下学期期末数学试题【全国百强校】黑龙江省大庆实验中学2017-2018学年高一6月月考数学(文)试题【市级联考】广西百色市2019届高三年级摸底调研考试数学理试题【市级联考】广西百色市2019届高三摸底调研考试数学文试题【市级联考】湖南省永州市2019届高三上学期第二次模拟考试数学(理)试题【全国百强校】宁夏银川一中2019届高三第一次模拟考试数学(理)试题宁夏银川一中2019届高三年级第二次模拟考试理科数学试题【全国百强校】安徽省太和中学2018-2019学年高一下学期第三次月考数学(文)试题安徽省皖东县中联盟2018-2019学年高一下学期期末数学试题(理)安徽省六安市毛坦厂中学2018-2019学年高一下学期期末考试数学(文)试题安徽省毛坦厂中学2018-2019学年高一下学期期末考试数学(理)试题安徽省阜阳市第三中学2018-2019学年高一下学期期末数学(文)试题安徽省阜阳市界首中学2019-2020学年高一上学期期末数学试题河南省新乡市第一中学2019-2020学年高一上学期12月月考数学试题湖南省长沙市明德中学2019-2020学年高三上学期11月第五次月考文科数学试题安徽省宣城市六校2019-2020学年高一下学期期末文科数学试题四川省眉山市眉山中学校2022-2023学年高二上学期期末数学文科试题黑龙江省七台河市勃利县高级中学2022-2023学年高一下学期期末数学试题
名校
3 . 如图,在
中,
,斜边
,
可以通过
以直线
为轴旋转得到,且平面
平面
.动点
在斜边
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/877f3020-1d2d-4822-b66b-82079bf1f3b8.png?resizew=116)
(1)求证:平面
平面
;
(2)当
为
的中点时,求异面直线
与
所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa3ed73c69ee962f2cbd1b9f62f38b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1df17440481c8da8e0a17f008dbc4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da6148304863f98ae409efdcf03af9d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa3ed73c69ee962f2cbd1b9f62f38b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1930e9c862abf8853321432cea3858fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ed01d1ff5a7f21a68fb3a1e5c7f393e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/877f3020-1d2d-4822-b66b-82079bf1f3b8.png?resizew=116)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95a55c40bb7437081d8e669974c8d1b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
2020-04-25更新
|
129次组卷
|
2卷引用:青海省西宁市城西区海湖中学2021-2022学年高二上学期数学第一次月考试题
名校
4 . 如图,
平面
,
,
交
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/eac558f9-7d07-4cd8-b961-9da5023adaff.png?resizew=152)
(1)证明:
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147e7c8ba0bbb540a712f6eb2ed6d22e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c949c8f299a3269f4bf279d67b46019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d86f1f70a7607c29440f7b851d2540.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2bb922b6dccd95a49847bb53908321c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/eac558f9-7d07-4cd8-b961-9da5023adaff.png?resizew=152)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e3f834d569575e10b7b7af40ff4548.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
您最近一年使用:0次
2020-03-31更新
|
460次组卷
|
4卷引用:青海省西宁市大通回族土族自治县2020-2021学年高二上学期期末联考数学(理)试题
青海省西宁市大通回族土族自治县2020-2021学年高二上学期期末联考数学(理)试题(已下线)专题04 空间向量与立体几何(单元测试卷)-2020-2021学年高中数学新教材人教A版选择性必修配套提升训练浙江省绍兴市2018-2019学年高二下学期期末数学试题湖南省长沙市雅礼实验中学2022-2023学年高三上学期入学考试数学试题
9-10高一下·河南郑州·期末
名校
解题方法
5 . 下列叙述中错误的是( )
A.若点P∈α,P∈β且α∩β=l,则P∈l |
B.三点A,B,C能确定一个平面 |
C.若直线a∩b=A,则直线a与b能够确定一个平面 |
D.若点A∈l,B∈l,且A∈α,B∈α,则l⊂α |
您最近一年使用:0次
2020-03-21更新
|
408次组卷
|
8卷引用:青海省西宁市普通高中五校2020-2021学年高二上学期期末联考数学(理)试题
青海省西宁市普通高中五校2020-2021学年高二上学期期末联考数学(理)试题北京市第一○一中学2021-2022学年高二上学期10月月考数学试题(已下线)2010年郑州盛同学校高一下学期期末考试数学卷(已下线)2012-2013年浙江台州六校高二上期中联考理科数学试卷北京西城13中2016-2017学年高二上期期中数学(文)试题安徽省合肥一中2018-2019学年高二上学期第一次段考数学(理)试题山西省晋中市平遥县综合职业技术学校2018-2019学年高二(普通班)上学期期中数学试题(已下线)8.4-8.6单元测试2【师说智慧课堂】新教材人教A(2019)必修(第二册)
6 . 如图,三棱柱
中,
底面
,点
是棱
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/999c1ef6-2719-42e8-a62c-91f394917831.png?resizew=148)
(Ⅰ)求证:
//平面
;
(Ⅱ)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ecf072589c0f901d92f6bda111d841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e486a1aad96167ff62f6fb5136e0bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e5a6afab22d5b53c1d8e87d58e8020.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/999c1ef6-2719-42e8-a62c-91f394917831.png?resizew=148)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(Ⅱ)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
您最近一年使用:0次
2020-03-17更新
|
272次组卷
|
2卷引用:青海省湟川中学2020-2021学年高二下学期第一次月考数学(文)试题
7 . 如图,多面体
中,平面
平面
,
,
四边形
为平行四边形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/9878dfdf-8ce8-4b57-8b55-e3e26bc758a9.png?resizew=182)
(1)证明:
;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ff27eea7545bb06f9472f91290c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a46fbde58e12b1edc038ae9e921722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4611ceb2a28f7a7e4d24266d7f99b22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/9878dfdf-8ce8-4b57-8b55-e3e26bc758a9.png?resizew=182)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aeeee5f39ee6f9c3ea01ada75d63b93.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33f4c358461db3633a818a52824b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fd680b3e2aeaba55e0b3b2486a0a3a8.png)
您最近一年使用:0次
2020-02-07更新
|
520次组卷
|
5卷引用:青海省西宁市大通回族土族自治县2020-2021学年高三上学期第一轮复习期末联考数学(理)试题
8 . 如图,多面体
中,平面
平面
,
,
,四边形
为平行四边形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/02b923dc-326b-4682-ab61-d86c1d5664b0.png?resizew=238)
(1)证明:
;
(2)若
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ff27eea7545bb06f9472f91290c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a46fbde58e12b1edc038ae9e921722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4611ceb2a28f7a7e4d24266d7f99b22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/02b923dc-326b-4682-ab61-d86c1d5664b0.png?resizew=238)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aeeee5f39ee6f9c3ea01ada75d63b93.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33f4c358461db3633a818a52824b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
您最近一年使用:0次
2020-02-07更新
|
185次组卷
|
2卷引用:青海省西宁市大通回族土族自治县2020-2021学年高三上学期第一轮复习期末联考数学(文)试题
名校
9 . 已知
,
,
是空间中的三条相互不重合的直线,给出下列说法:①若
,
,则
;②若
与
相交,
与
相交,则
与
相交;③若
平面
,
平面
,则
,
一定是异面直线;④若
,
与
成等角,则
.其中正确的说法是______ (填序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d553efed052e7e0777728ef622a5c39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce590e7dd367445634136518979dc5b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c416e5fcd84ae9a287348fbecb625706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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2019-12-18更新
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13卷引用:青海省西宁市城西区海湖中学2021-2022学年高二上学期数学第一次月考试题
青海省西宁市城西区海湖中学2021-2022学年高二上学期数学第一次月考试题(已下线)第十一章 立体几何初步 11.3 空间中的平行关系 11.3.1 平行直线与异面直线人教A版高中数学必修二2.1.2空间中直线与直线之间的位置关系2广西柳州市第二中学2019-2020学年高一上学期11月月考数学试题人教A版(2019) 必修第二册 突围者 第八章 第五节 课时1 直线与直线平行(已下线)【新教材精创】11.3.1平行直线与异面直线练习(1)(已下线)8.5.1 直线与直线平行(课后作业)【师说智慧课堂】新教材人教A(2019)必修(第二册)沪教版(2020) 必修第三册 经典导学 第10章 10.2 第1课时 空间的平行直线(已下线)第28讲 直线与直线平行 2(已下线)8.5.1直线与直线平行(精讲)-【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)10.2 直线与直线间的位置关系(第1课时)(四大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)(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)专题13.3空间两条直线的位置关系-重难点突破及混淆易错规避(苏教版2019必修第二册)
10 . 在四棱锥
中,
平面
,
∥
,
,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/f48284d6-56f1-4713-8d37-d2e468ff4a16.png?resizew=187)
(1)求证:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求证:平面
平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf15f23e8531a3127fa09b9a8dacab6a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/f48284d6-56f1-4713-8d37-d2e468ff4a16.png?resizew=187)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/689c065652544780be8b33ae92cbb6d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
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2019-12-17更新
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7卷引用:青海省西宁市城西区海湖中学2021-2022学年高二上学期数学第一次月考试题