1 . 在三棱锥
中,
,
,
,
,
分别为棱
的中点.现有以下3个结论:①三棱锥
的外接球表面积为
;②
;③
平面
.则其中正确结论的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c986d2a9857d425dc2c62b034dcfd34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4e66a2c8440276c9608a8abe834083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dee6c1410e79934b560642684807e70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fc5f2856d1c952464453577bd1cc268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceeb10380ea1162ae9078c9b93adb846.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a39dce3f1e36dbe01293c309816968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b0e8d6874ca0163575176a49accf45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d07d16fc91aa960b67ba4b474de8a62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05a270ec7e23fc0cc1d4b04bf1d22184.png)
您最近一年使用:0次
2 . 在三棱锥
中,
,
分别为棱
的中点.现有以下4个结论:
①三棱锥
的外接球表面积为
;
②
;
③
平面
;
④当
时,平面
平面
.
则其中正确结论的序号为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e561abd2bb54ac40d4f7af31ff9f7397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96c92bc20565fb976e0c73ee4017261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceeb10380ea1162ae9078c9b93adb846.png)
①三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a39dce3f1e36dbe01293c309816968.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b0e8d6874ca0163575176a49accf45.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d07d16fc91aa960b67ba4b474de8a62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05a270ec7e23fc0cc1d4b04bf1d22184.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3755b2bcf7516eedb26a27ad73657216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
则其中正确结论的序号为
您最近一年使用:0次
名校
3 . 已知棱长为1的正方体
,过对角线
作平面
交棱
于点
,交棱
于点
,则:①平面
分正方体所得两部分的体积相等;②四边形
一定是平行四边形;③平面
与平面
不可能垂直; ④四边形
的面积的最大值为
.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/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef5ea43614d815c3abb27a42dfb101b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1477ae90a240deba97f8dadf4d7c41aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef5ea43614d815c3abb27a42dfb101b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
您最近一年使用:0次
2020-09-12更新
|
183次组卷
|
2卷引用:四川省成都石室中学2020-2021学年高三上学期开学考试数学(理)试题
名校
4 . 已知
、
是异面直线,给出下列结论:
①一定存在平面
,使直线
平面
,直线
平面
;
②一定存在平面
,使直线
平面
,直线
平面
;
③一定存在无数个平面
,使直线
与平面
交于一个定点,且直线
平面
.
则所有正确结论的序号为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
①一定存在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe623bd25476a860fa4c2a179b81464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edaf5492ffc6db02fd5968b643c8b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
②一定存在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764b59b077bda19d131095b454942d6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edaf5492ffc6db02fd5968b643c8b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
③一定存在无数个平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edaf5492ffc6db02fd5968b643c8b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
则所有正确结论的序号为( )
A.①② | B.② | C.②③ | D.③ |
您最近一年使用:0次
2020-03-21更新
|
448次组卷
|
3卷引用:江苏省南通市2019-2020学年高二上学期期初调研测试数学试题
名校
解题方法
5 . 已知四边形ABCD为矩形,AB=2AD=4,M为AB的中点,将△ADM沿DM折起,得到四棱锥A1﹣DMBC,设A1C的中点为N,在翻折过程中,得到如下有三个命题:①BN∥平面A1DM;②三棱锥N﹣DMC的最大体积为
;③在翻折过程中,存在某个位置,使得DM⊥A1C.其中正确命题的序号为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e7aef79a09a1089d46c58636724fd9c.png)
您最近一年使用:0次
2020-02-13更新
|
286次组卷
|
2卷引用:上海市七宝中学2022-2023学年高二上学期开学考数学试题
名校
6 . 对于四面体
,以下说法中,正确的序号为_______ (多选、少选、选错均不得分).
①若
,
,
为
中点,则平面
⊥平面
;
②若
,
,则
;
③若所有棱长都相等,则该四面体的外接球与内切球的半径之比为2:1;
④若以
为端点的三条棱所在直线两两垂直,则
在平面
内的射影为
的垂心;
⑤分别作两组相对棱中点的连线,则所得的两条直线异面.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532aece6cfd67e2a97977eed978dbf2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97a9b32570d553161be04d13954e92a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77e3c1c236141d6118429fade0a9b9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d72a007e3c4a134956b0e3fbde5f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70734a8e672376bb0bd1522e229f86a2.png)
③若所有棱长都相等,则该四面体的外接球与内切球的半径之比为2:1;
④若以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df6d51738ac1bc8b9530ea4a55745c2.png)
⑤分别作两组相对棱中点的连线,则所得的两条直线异面.
您最近一年使用:0次
2016-12-03更新
|
887次组卷
|
3卷引用:辽宁省沈阳市东北育才学校2014-2015学年高一下学期期初数学试题
名校
7 . 已知
是两条不同的直线,
是两个不重合的平面,给出下面三个结论:
①若
,则
;
②若
,则
;
③若
是两条异面直线,且
,则
.
其中正确结论的序号为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44c7c553d0f15facbbd2f35bc728d32b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa404d3ff313b0a28a76a48d7d87234.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e0fb84642a490c9fad486d7271041a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0258342fb0eff42b5d37cbe42b6c89b.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de42f52fe4cb94b197174f88e7b1b425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de666db0febae223cc4d1dc189d71ca6.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44c7c553d0f15facbbd2f35bc728d32b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13fecbd35aa1a6f16c4e6b75557189a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de666db0febae223cc4d1dc189d71ca6.png)
其中正确结论的序号为
A.①② | B.①③ | C.②③ | D.③ |
您最近一年使用:0次
2019-06-07更新
|
1633次组卷
|
4卷引用:北京市平谷区第五中学2020-2021学年高二上学期开学考试数学试题
北京市平谷区第五中学2020-2021学年高二上学期开学考试数学试题人教A版 全能练习 必修2 第二章 第二节 2.2.2平面与平面平行的判定(已下线)理科数学-2021年高考考前20天终极冲刺攻略(三)(课标全国卷)(5月26日)贵州省贵阳市第一中学2023-2024学年高一下学期教学质量监测卷(三)数学试题
名校
解题方法
8 . 已知正四棱柱
的底面边长为2,侧棱
为上底面
上的动点,给出下列四个结论:
①若PD=3,则满足条件的P点有且只有一个;
②若
,则点P的轨迹是一段圆弧;
③若PD∥平面
,则DP长的最小值为2;
④若PD∥平面
,且
,则平面BDP截正四棱柱
的外接球所得图形的面积为
.
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/b48eab2e9070bf8d094193ea52f1129a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
①若PD=3,则满足条件的P点有且只有一个;
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71826134c3080aa75becc655a9089855.png)
③若PD∥平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cfdc6224181d44e63aab43ddaf07ef.png)
④若PD∥平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cfdc6224181d44e63aab43ddaf07ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71826134c3080aa75becc655a9089855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b2dfd7c4a190b8dbbc56f2fcc2b2ce0.png)
其中所有正确结论的序号为
您最近一年使用:0次
2019-01-21更新
|
822次组卷
|
4卷引用:广东省东莞市光明中学2021届高三下学期期初考试数学试题
名校
9 . 给出下列叙述:
①正四面体
的棱长为
,
是棱
的中点,则异面直线
与
所成角的余弦值是
;
②在等比数列
中前
项和为
,前
项和为
,则前
项和为
;
③直线
关于直线
对称的直线方程为
;
④若
,
,且
,则
的最小值为
;
其中所有正确叙述的序号是_____________ .
①正四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a8b76e36783a69d14ec54af82c7df0.png)
②在等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53c7539ed297ea63b9ace6f5cc58ca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad491e5b5e14c49ef8b7004ebcfcef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade9841a8e6840efddcfd8620a6fc1fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88b4213192069c5c22e7c97f6242c11.png)
③直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/056e249d0c33ef92b956f84937fa9324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35dd2b23130371b570ed71f8a6e23311.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f503de26e16e1a0ab7be45df505e1c2.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/637a04c9fd4fb91fd89e60aca2f86b4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c633cc3cfa5df8130f87f78b32ce38dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc0d80fd60126ee6128f67a8e87a926c.png)
其中所有正确叙述的序号是
您最近一年使用:0次
10-11高一下·辽宁大连·开学考试
10 . 下列命题中,正确命题的序号为
①平行于同一平面的两个平面平行; ②垂直于同一平面的两条直线平行;
③垂直于同一直线的两平面平行; ④平行于同一平面的两平面平行;
⑤垂直于同一平面的两个平面平行;
⑥如果两个平面垂直,过一个平面内一点作交线的垂线,则它就垂直于另一个平面;
⑦如果一个平面内的相交直线平行另一个平面内的两条相交直线,则这两个平面平行;
⑧如果一个平面过另一个平面的垂线,则这两个平面垂直.
①平行于同一平面的两个平面平行; ②垂直于同一平面的两条直线平行;
③垂直于同一直线的两平面平行; ④平行于同一平面的两平面平行;
⑤垂直于同一平面的两个平面平行;
⑥如果两个平面垂直,过一个平面内一点作交线的垂线,则它就垂直于另一个平面;
⑦如果一个平面内的相交直线平行另一个平面内的两条相交直线,则这两个平面平行;
⑧如果一个平面过另一个平面的垂线,则这两个平面垂直.
A.①②③④⑦⑧ | B.①③⑤⑥ | C.①②④⑥ | D.①④⑦ |
您最近一年使用:0次