名校
解题方法
1 . 在正方体
中,棱长为1,
,
分别为
,
的中点,
为线段
上异于
,
的动点,现有下列结论:
①
与
为异面直线;
②
;
③
周长的最小值为
;
④三棱锥
的体积为定值.
其中所有正确结论的编号是_______ .
![](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/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554b3b4c5ce7aca81becc07ed4903736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09e7941b72b636ca831338ec7a239040.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfcfff898f2b0c676e8348635df102d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54c276c0d445c7c5965d22fea2492e74.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1a811539a6c82ce6ef87ca2e602c65a.png)
其中所有正确结论的编号是
您最近一年使用:0次
2021-07-29更新
|
280次组卷
|
2卷引用:四川省绵阳市2020-2021学年高二下学期期末数学(理科)试题
名校
解题方法
2 . 如图,在正四棱锥
中,
,
,
分别是
,
,
的中点,动点
在线段
上运动时,下列四个结论:①![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4862958e60c245dc9a5d9cb57d31eb4.png)
;②
;③
面
;④
面
中恒成立的为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4862958e60c245dc9a5d9cb57d31eb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d1aba56e04a373cefa813b31a3d99f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3834a4bb20d2b065695dbf53091b065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5000fea066102e62cf2128ccbbd2b3e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4862958e60c245dc9a5d9cb57d31eb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc6f6dfdbe7d39891c35f67e1a95c7f.png)
![](https://img.xkw.com/dksih/QBM/2021/3/14/2677868871032832/2685640297308160/STEM/945388bc535740a5a28b5a810acd4e74.png?resizew=174)
您最近一年使用:0次
2021-03-25更新
|
177次组卷
|
2卷引用:四川省乐山沫若中学2020-2021学年高二下学期入学考试数学(文科)试题
名校
解题方法
3 . 如图,三棱柱
中,侧棱
底面
,
外接球的球心为
,点
是侧棱
上的一个动点,有下列判断:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/20/ae97840c-32d0-4230-b51a-dcbaaa0941fc.png?resizew=187)
①直线
与直线
是异面直线;
②
一定不垂直于
;
③三棱锥
的体积为定值;
④
的最小值为
.
其中正确的序号是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e229fda1d2925e461d640551682c192.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/20/ae97840c-32d0-4230-b51a-dcbaaa0941fc.png?resizew=187)
①直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e516121599c9fcc528121c00afcf52fc.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
③三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02dd76b7dbe2d9ea408dcac787f89d2d.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f998e8cbd8c96e88a6825bf610021970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
其中正确的序号是
您最近一年使用:0次
解题方法
4 . 如图表示正方体表面的一种展开图,则其中的四条线段
在原正方体中为异面直线且所成角为
的有__________ 对.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e5814f442d97f3a050e28ec0ca66f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/50dae0b7-7bb1-4cf2-9108-689c430a5f1f.png?resizew=135)
您最近一年使用:0次
2018-01-11更新
|
447次组卷
|
2卷引用:四川省广安、眉山2018届毕业班第一次诊断性考试数学(理)试题
名校
解题方法
5 . 如图,平面
与平面
相交于
,
,点
,点
,则下列叙述错误的是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e80859ae41f82e2dd738272c2bb44c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/affe0e1cb13a79f80f48c14674648ab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b55b9f6ff7cc353d1d40ea3919857213.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/9/35dae176-a196-476c-99bb-b839a9cfd8d6.png?resizew=147)
A.直线AD与BC是异面直线 |
B.过AD只能作一个平面与BC平行 |
C.过AD只能作一个平面与BC垂直 |
D.过D只能作唯一平面与BC垂直,但过D可作无数个平面与BC平行 |
您最近一年使用:0次
2018-04-23更新
|
467次组卷
|
3卷引用:四川省资阳市2018届高三4月模拟考试(三诊)数学(文)试题
6 . 如图是一几何体的平面展开图,其中
为正方形,
,
分别为
,
的中点,在此几何体中,给出下面四个结论:①直线
与直线
异面;②直线
与直线
异面;③直线
平面
;④平面
平面
.
其中一定正确的选项是
![](https://img.xkw.com/dksih/QBM/2018/1/2/1851643074822144/1852494955667456/STEM/dd02474aad9c4972b7470ea7781913a4.png?resizew=137)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39282bdf319f30d7bc261e2e3ab3b1e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
其中一定正确的选项是
![](https://img.xkw.com/dksih/QBM/2018/1/2/1851643074822144/1852494955667456/STEM/dd02474aad9c4972b7470ea7781913a4.png?resizew=137)
A.①③ | B.②③ | C.②③④ | D.①③④ |
您最近一年使用:0次
2018-01-03更新
|
378次组卷
|
2卷引用:四川省石室中学2017-2018学年高二上学期半期考试数学(文)试题
名校
7 . 如图是正方形的平面展开图.在这个正方体中,
①
与
是异面直线;
②
与面
平行;
③
与面
所成角的正切值是
;
④
与
垂直.
以上四个命题中,正确命题的序号是__________ .
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43819ab7b268a6293a9251935b594690.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5134881ab384b39b1b1adabe05b9c74c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
以上四个命题中,正确命题的序号是
![](https://img.xkw.com/dksih/QBM/2017/8/14/1751785702260736/1751921621180416/STEM/65c293d3f76c4ce5a654946e500c1518.png?resizew=219)
您最近一年使用:0次
12-13高二上·四川资阳·期末
解题方法
8 . 如图,点P在长方体
的面对角线
(线段
)上运动,给出下列四个命题:
①直线AD与直线
为异面直线;
②恒有
面
;
③三棱锥
的体积为定值;
④当长方体各棱长都相等时,面
面
.
其中所有正确命题的序号是_________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dfda77ecf61013170a6f43b4d9d116.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
①直线AD与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655c413f509068d30b165f9d92bdba0.png)
②恒有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f86e2d69b11402d9d6cbb06e057778a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
③三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad99ef5e70de37345c708b758d545f.png)
④当长方体各棱长都相等时,面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecb955df71b56b325021d2552303285f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
其中所有正确命题的序号是
![](https://img.xkw.com/dksih/QBM/2012/2/7/1570719944933376/1570719950307328/STEM/bbf9036c-653e-4a79-bf1b-6680b5de340b.png?resizew=201)
您最近一年使用:0次
9-10高二下·四川绵阳·期中
解题方法
9 . 在正方体
中,
分别是线段
的中点,以下结论:①
丄
;②
与
异面;③
丄面
;其中正确的是( )
![](https://img.xkw.com/dksih/QBM/2010/4/29/1569709163315200/1569709167878144/STEM/f2dba7c6dc964bafabe7865f2b5d3041.png?resizew=157)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414d12245deeef36206d85a42dd7a853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679d44b754580b0450b5b06784df5af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bf9ef324f1289e205e29fed105c38e.png)
![](https://img.xkw.com/dksih/QBM/2010/4/29/1569709163315200/1569709167878144/STEM/f2dba7c6dc964bafabe7865f2b5d3041.png?resizew=157)
A.① | B.①② | C.①③ | D.②③ |
您最近一年使用:0次