1 . 如图,矩形
中,
,N为边
的中点,将
沿
翻折成
(
平面
),M为线段
的中点,则在
翻折过程中,下列命题:①与平面
垂直的直线必与直线
垂直;②线段
的长为
;③异面直线
与
所成角的正切值为
;④当三棱锥
的体积最大时,三棱锥
外接球表面积是
.正确的个数为( )
![](https://img.xkw.com/dksih/QBM/2020/5/2/2453948648873984/2454881345044480/STEM/a463dcebe5354aab98c6afc81628ef2d.png?resizew=193)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d58da37b3d1dbd2fee75089d5ba28134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7ad41b36674fd6e90176ee24cdefbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4c2abf2e18c55050f3a41399c05a619.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b08323318c6ec653017546cb9927800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7ad41b36674fd6e90176ee24cdefbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a01298ec90ac8bc0fe14d04068fcd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afae866ce76faf4828da4bc0b78e2f03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f2b010fb609768bcf756e99b0ce8cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f2b010fb609768bcf756e99b0ce8cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9609625b502348556ff8ba32deac8caa.png)
![](https://img.xkw.com/dksih/QBM/2020/5/2/2453948648873984/2454881345044480/STEM/a463dcebe5354aab98c6afc81628ef2d.png?resizew=193)
A.1个 | B.2个 | C.3个 | D.4个 |
您最近一年使用:0次
解题方法
2 . 已知
是由具有公共直角边的两块直角三角板(
和
)组成的三角形,如下图所示,其中
,
.现将
沿斜边
进行翻折成
(
不在平面
上).若
分别为
和
的中点,则在
翻折过程中,下列命题中错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ee908ab941762e7a567e8434199d618.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0773ef97c87725335faeaa95163e9121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2bdcd23d2c26d9df0b4756d8a715673.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ec435aa1401dbce7863b531bf2f3e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ee908ab941762e7a567e8434199d618.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d151f8296e8f9ba83d1f7d5207428ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f8f01137e92c0f2e63467036ae9cce.png)
A.在线段![]() ![]() ![]() ![]() |
B.存在某个位置,使得直线![]() ![]() |
C.存在某个位置,使得直线![]() ![]() ![]() |
D.对于任意位置,二面角![]() ![]() ![]() |
您最近一年使用:0次
名校
3 . 如图,矩形
中,
,
为边
的中点,将
沿直线
翻折成
,若
为线段
的中点,则在
翻折过程中,下面四个命题中是真命题的序号是______ .
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/9e71f32d-7fae-46e1-a0dd-537aa258f556.png?resizew=209)
(1)存在某个位置,使![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2181c78134c310f746eab44b9124e63b.png)
(2)存在某个位置,使![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb494e5b0c2e0f0652f2d87a9291d61b.png)
(3)存在某个位置,使
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
(4)存在某个位置,使
与平面
所成角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c4e4a162f12d12a082b8d8fdd1aeab9.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/f460edcced5597615113c0fdc95b1dfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f07107087ce4abdfa5fc68fe6fb62f7.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/f460edcced5597615113c0fdc95b1dfc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/9e71f32d-7fae-46e1-a0dd-537aa258f556.png?resizew=209)
(1)存在某个位置,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2181c78134c310f746eab44b9124e63b.png)
(2)存在某个位置,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb494e5b0c2e0f0652f2d87a9291d61b.png)
(3)存在某个位置,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d8d90d123fec1ae1b7b30dac9f88e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
(4)存在某个位置,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
您最近一年使用:0次
4 . 如图,平面
与平面
所成的二面角是
,
是平面
内的一条动直线,
,则直线
与
所成角的正弦值的取值范围是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/5d218356-25b6-46f0-935c-afe11ccfbecc.png?resizew=151)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b312dab930cbbb9a4bb1a99f044dab73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b312dab930cbbb9a4bb1a99f044dab73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da2ef20a46cff5280987ba741705a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/5d218356-25b6-46f0-935c-afe11ccfbecc.png?resizew=151)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2020-04-14更新
|
833次组卷
|
2卷引用:浙江省衢州市2017-2018学年高二下学期期末数学试题
解题方法
5 . 如图,在三棱锥
中,
,
,
,
,
为线段
的中点,
为线段
上一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/7eea6f27-89ef-4ff0-86dc-3b8a4fc7d4c0.png?resizew=191)
(1)求证:
;
(2)当
平面
时,若三棱锥
的体积为
,求
值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbb05b8b630052ff544249ebd72d95d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a15a004f7d47ed595f063e60075223a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c88b2cf75a92be236757bce120d5100d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/7eea6f27-89ef-4ff0-86dc-3b8a4fc7d4c0.png?resizew=191)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b07e317ffe7859e81b42ef4970e344a.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42020cfacd62b300cad053981bab9e0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2020-04-12更新
|
690次组卷
|
2卷引用:中原金科大联考2019-2020学年高三4月质量检测数学(文)试题
6 . 若点
为点
在平面
上的正投影,则记
.如图,在棱长为1的正方体
中,记平面
为
,平面
为
,点
是线段
上一动点,
.给出下列四个结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/e7698bca-581b-41a0-bfc5-861d095fc98b.png?resizew=220)
①
为
的重心;
②
;
③当
时,
平面
;
④当三棱锥
的体积最大时,三棱锥
外接球的表面积为
.
其中,所有正确结论的序号是________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4fac2a8beadd8dbe0944cfa9f4286f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae7f4612c548b1f72a964ddb291cd2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7774c6fb47fdf109a97125cce139c81.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/e7698bca-581b-41a0-bfc5-861d095fc98b.png?resizew=220)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae863e7a1f1fed09f1075de4a817c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891b72156544758442245afbaa566c22.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41a4cf13df912766157430d8417867d4.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/313da017bcb0535ad3a099b536cb1703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0df762247711e7bdf39ff50003813b06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
④当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/023fd92b813d8911258409d7540825cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/023fd92b813d8911258409d7540825cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9fdc1f8ed0ae44b54a9a2a3aca2db4.png)
其中,所有正确结论的序号是
您最近一年使用:0次
解题方法
7 . 已知正方体
的棱长为
,点
分别为棱
的中点,下列结论中,其中正确的个数是( )
![](https://img.xkw.com/dksih/QBM/2020/3/18/2422133625020416/2422937541246976/STEM/f308309661f44757959ca132692726ce.png?resizew=175)
①过
三点作正方体的截面,所得截面为正六边形;
②
/平面
;
③
;
④异面直线
与
所成角的正切值为
;
⑤四面体
的体积等于![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aec67c4c83e4955f36ec34afb19df83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029ed096f249bfec4420d746e9a3d292.png)
![](https://img.xkw.com/dksih/QBM/2020/3/18/2422133625020416/2422937541246976/STEM/f308309661f44757959ca132692726ce.png?resizew=175)
①过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efd3ad8ddccdc251c85533353d2633f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c769b97e5ec2b6e6bac800c64f77cec.png)
④异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
⑤四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ac02c2f91cadb1e328bc6ab9b9c491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aec67c4c83e4955f36ec34afb19df83.png)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
解题方法
8 . 已知正方体
的棱长为
,
,
,
分别是棱
,
,
的中点,给出下列四个命题:
①
;
② 直线
与直线
所成角为
;
③ 过
,
,
三点的平面截该正方体所得的截面为六边形;
④ 三棱锥
的体积为
.
其中,正确命题的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d435974639ea2850bb5c21efe64b123b.png)
② 直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/260200d547998bcac50a4a491382e7f4.png)
③ 过
![](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)
④ 三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b2c673e86dc8bf49f3b34256ee79679.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c6c7567972273b4ba733b47bf9d5408.png)
其中,正确命题的个数为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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2020-03-29更新
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1253次组卷
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7卷引用:2020届广东省广州市高三3月阶段训练(一模)数学(文)试题
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9 . 如图,矩形ABCD中,AB=2AD=2,E为边AB的中点,将△ADE沿直线DE翻折成△
DE,使平面
DE⊥平面BCDE,若M为线段
C的中点,下面四个命题中不正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/b8237c68-db99-4a6b-86a3-37301bf000c6.png?resizew=176)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/b8237c68-db99-4a6b-86a3-37301bf000c6.png?resizew=176)
A.BM![]() ![]() | B.CE⊥平面![]() |
C.DE![]() | D.平面![]() ![]() |
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10 . 已知正方体
的棱长为
,点
分别棱楼
的中点,下列结论中正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/72782c69-c1f9-4773-bd10-8583f25d22da.png?resizew=199)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029ed096f249bfec4420d746e9a3d292.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/72782c69-c1f9-4773-bd10-8583f25d22da.png?resizew=199)
A.四面体![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.异面直线![]() ![]() ![]() |
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2020-03-15更新
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6卷引用:福建省福州第一中学2019-2020学年高二上学期期末数学试题