名校
1 . 如图,多面体
中,面
为正方形,
平面
,
,且
,
,
为棱
的中点,
为棱
上的动点,有下列结论:
①当
为
的中点时,
平面
;
②存在点
,使得
;
③当
为
的中点时,直线GH与BE所成角的余弦值为
;
④三棱锥
的外接球的表面积为
.
其中正确的结论序号为______ .(填写所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1019c0405370c673e37b46c066eba839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c7e72ef83184b96b12a51daf32c220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95893879ed5feeef3cb2cf68a1a88632.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3362a45b72536c714c5107b0ae94f1c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c6e7c025362c46a64a8956761f08e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/22/b4af39c4-b247-4220-b17e-46dd0451f435.png?resizew=164)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c6e7c025362c46a64a8956761f08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4193fb98c610f41f9a6c89d046f13d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d09072f5be97caf5e942ae8fc16b0bf.png)
②存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3f8b5c2dba20d42a8c551cd75a38fe.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c6e7c025362c46a64a8956761f08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c14ff9b66f21c05e52dc3c8908c2df.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f26712d1a7a5864cd18498f16f7bd96c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e95a79288fcb7e47fba4410722e2bc6.png)
其中正确的结论序号为
您最近一年使用:0次
名校
2 . 如图,矩形
中,
,
为边
的中点,将
沿直线
翻折至
的位置.若
为线段
的中点,在
翻折过程中(
平面
),给出以下结论:
①三棱锥
体积最大值为
;
②直线
平面
;
③直线
与
所成角为定值;
④存在
,使
.
则其中正确结论的序号为_________ .(填写所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80f51c31583fea58fde645474d60b8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa2a83fed9bf4cb09d84a980452e346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8588e18e27bfebf7c81c7e3c7efb1149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
①三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb79f948d408ab4fb6708bde172c5e5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11b9f96b8ecc3cb000bb2f030809f225.png)
②直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c70966a318ef8ecf874257f5c5e5db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
③直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
④存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa2a83fed9bf4cb09d84a980452e346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2181c78134c310f746eab44b9124e63b.png)
则其中正确结论的序号为
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/2/db8c3c80-3639-479e-8ae4-e7aeaef6394b.png?resizew=239)
您最近一年使用:0次
2022-07-01更新
|
1369次组卷
|
5卷引用:山西省太原市2021-2022学年高一下学期期末数学试题
3 . 给出下列结论:
①设平面α与平面β相交于直线m,直线a在平面α内,直线b在平面β内,且b⊥m,则α⊥β是a⊥b的必要不充分条件.
②在区间[-1,1]上随机取一个数x,则
的值介于0到
之间的概率为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
③从以正方体的顶点连线所成的直线中任取两条,则所取两条直线为异面直线的概率为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f053ede9bc7e812d21128cc31a59ad3.png)
④将4个相同的红球和4个相同的蓝球排成一排,从左到右每个球依次对应的序号为1,2,3,…,8,若同色球之间不加区分,则4个红球对应的序号之和小于4个蓝球对应的序号之和的排列方法种数为31.
其中正确结论的序号为___________ .
①设平面α与平面β相交于直线m,直线a在平面α内,直线b在平面β内,且b⊥m,则α⊥β是a⊥b的必要不充分条件.
②在区间[-1,1]上随机取一个数x,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e51b2fb9409bd4790ca95eb01fa8d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
③从以正方体的顶点连线所成的直线中任取两条,则所取两条直线为异面直线的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f053ede9bc7e812d21128cc31a59ad3.png)
④将4个相同的红球和4个相同的蓝球排成一排,从左到右每个球依次对应的序号为1,2,3,…,8,若同色球之间不加区分,则4个红球对应的序号之和小于4个蓝球对应的序号之和的排列方法种数为31.
其中正确结论的序号为
您最近一年使用:0次
名校
4 . 已知正方体
的棱长为2,
为体对角线
上的一点,且
,现有以下判断:①
;②若
平面
,则
;③
周长的最小值是
;④若
为钝角三角形,则
的取值范围为
,其中正确判断的序号为______ .
![](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/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bd250fb1bebe4f610c7fe281217b38b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c040eb3985b66e8db65932fdb63f844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4645450a006f2c20087486d0833afbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c3ea872a20fdc1843cb5ffce8a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ab13ef156d034b710d811e09b0be34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b590aaed2d5ef2610aa608faf95c02ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ab13ef156d034b710d811e09b0be34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64fcec77177443519207ffc6afb988d0.png)
您最近一年使用:0次
2019-12-10更新
|
570次组卷
|
3卷引用:重庆市渝中区巴蜀中学2019-2020学年高三“一诊”模拟测试卷数学(理)试题
10-11高一下·海南·期末
5 . 如图是正方体的表面展开图,在这个正方体中有如下命题:
①AF∥NC;
②BE与NC是异面直线;
③AF与DE成60°;
④AN与ME成45°.
其中正确命题的序号为______ (填正确命题的序号)
①AF∥NC;
②BE与NC是异面直线;
③AF与DE成60°;
④AN与ME成45°.
其中正确命题的序号为
![](https://img.xkw.com/dksih/QBM/2011/4/18/1570121800425472/1570121805701120/STEM/b585ed4d1d67487baca0095361b0cdaa.png?resizew=230)
您最近一年使用:0次
名校
解题方法
6 . 如图,正方体
的棱长为1,E,F,G分别为
的中点,则下列说法正确的序号为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/f4445050-0ae4-4d14-852a-354b62e652d7.png?resizew=220)
①直线
与直线
所成角的正切值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
②直线
与平面
不平行
③点C与点G到平面
的距离相等
④平面
截正方体所得的截面面积为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4700efcb84c4027ce7a50af0d5212fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473ce0e22c4edc6ef768e0c12f59e483.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/f4445050-0ae4-4d14-852a-354b62e652d7.png?resizew=220)
①直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04777f3f4661fa1c08a1cc0dfb807c7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
②直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04777f3f4661fa1c08a1cc0dfb807c7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
③点C与点G到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
④平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4700efcb84c4027ce7a50af0d5212fc.png)
A.①④ | B.②③ | C.①③ | D.②④ |
您最近一年使用:0次
7 . 如图所示的菱形
中,
对角线
交于点
,将
沿
折到
位置,使平面
平面
.以下命题:
①
;
②平面
平面
;
③平面
平面
;
④三棱锥
体积为
.
其中正确命题序号为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e4b6f03fa7c782408bb6fabb57c1576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3c032441543354c154ee67d744abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ea25ef38e4afa8f75ffd0842890289.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe052786101dfcc941480919eb2cecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/22/70dc5fdb-9d52-4f09-87d1-32477e72c148.png?resizew=342)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c83a968964b21bd831d75905ca1e487.png)
②平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0cf578c7ba542ff9946ad172f896dfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
③平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53d138354c4e021ac8ae2a2fb176ca14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1530d93834fbafba5f7217778ea90442.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb4c6e9a723aa843e6ba62d7c1a3a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
其中正确命题序号为( )
A.①②③ | B.②③ | C.③④ | D.①②④ |
您最近一年使用:0次
2023-05-19更新
|
1248次组卷
|
6卷引用:陕西省咸阳市2023届高考模拟理科数学试题
陕西省咸阳市2023届高考模拟理科数学试题陕西省咸阳市2023届高考模拟文科数学试题山西省太原师范学院附属中学、太原市师苑中学校2022-2023学年高一下学期5月月考数学试题江西省南昌市铁路第一中学2023-2024学年高二上学期10月月考数学试题(已下线)第04讲 直线、平面垂直的判定与性质(五大题型)(讲义)(已下线)第一章 点线面位置关系 专题二 空间垂直关系的判定与证明 微点5 平面与平面垂直的判定与证明【基础版】
8 . 如图,在正方体
中,M,N,P,Q分别是
,
,AB,
的中点,给出下列四个判断:
①
平面PMN;
②PN与QM所成的角为60°;
③点B,D到平面PMN的距离相等;
④平面PMN截该正方体的截面为正六边形.则正确的序号为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f647de53756993a680347e8ce3c0f0.png)
②PN与QM所成的角为60°;
③点B,D到平面PMN的距离相等;
④平面PMN截该正方体的截面为正六边形.则正确的序号为
![](https://img.xkw.com/dksih/QBM/2022/4/16/2959450596941824/2961377360592896/STEM/6bebcc7badc246b8b6637146deda6cc1.png?resizew=210)
您最近一年使用:0次
解题方法
9 . 如图,在棱长为2的正方体
中,点M在线段
(不包含端点)上运动,则下列4个命题中所有正确命题的序号为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/14/d650b741-bd5e-4d45-8d28-b0924590a947.png?resizew=167)
①异面直线
与
所成角的取值范围是
;
②
;
③三棱锥
的体积为定值
;
④
的最小值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/14/d650b741-bd5e-4d45-8d28-b0924590a947.png?resizew=167)
①异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bc08d14fe6bc48674b8c3b2d464fc88.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ba3d4adb389c1d4ae5b742372440d5.png)
③三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6557d0725272b008c5969c0a203aa10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d599cb4a589f90b0205f24c2e1fa021e.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82aeb9ae6660cf9bd7b2f57ff4a47ef4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfba144ad36e04d7032e30b08413cda3.png)
A.②④ | B.①④ | C.②③④ | D.①③ |
您最近一年使用:0次
10 . 如图,已知二面角
的棱l上有A,B两点,
,
,
,
,若
,
,有以下结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/31/27d139f7-0857-41b8-85e9-3fdd535e919c.png?resizew=182)
(1)直线AB与CD所成角的大小为
;
(2)二面角
的大小为
;
(3)三棱锥
的体积为
;
(4)直线CD与平面
所成角的正弦值为
.
则正确结论的序号为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4cc2f3dcb248fc764614be3a9ddd25b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c638fb895acd987140d0ca6bef097499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaccf1887c4b530fd86a2f0f199c6797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb0a2d7d40a6c0bf1fddb802db381689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e9b9d23b4f8dd581461004689d0b863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/321f96c4f808afe67cf565ca74ae0351.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/31/27d139f7-0857-41b8-85e9-3fdd535e919c.png?resizew=182)
(1)直线AB与CD所成角的大小为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
(2)二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
(3)三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(4)直线CD与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa42621cd6793e7f3673fdb49bc3123.png)
则正确结论的序号为
您最近一年使用:0次
2022-07-18更新
|
654次组卷
|
4卷引用:山东省菏泽市2021-2022学年高一下学期期末数学试题
山东省菏泽市2021-2022学年高一下学期期末数学试题(已下线)专题强化训练四 直线与平面所成的角、二面角的平面角的常见解法(2)-《考点·题型·技巧》(已下线)模块四 专题2 期末重组综合练(山东)陕西省西安市西咸新区泾河新城第一中学2022-2023学年高一下学期5月质量检测数学试题