解题方法
1 . 如图所示,正方体
的棱长为1,
分别是棱
的中点,过直线
的平面分别与棱
交于
,恰出以下四个命题:
①平面
一定为矩形; ②平面
平面
;
③当
为
的中点时,
的面积最小; ④四棱锥
的体积为常数.
以上命题中正确命题的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18a99be053c95aefbebe7460e50df572.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7ad4ab6413ee1fb338ad0c632df6f60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed75232f4fb7eae7ee84d8049a2e1565.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
①平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e92eac740953aa383be636ea90fd47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c1f56858867e7b6becaeac49112a3d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cb36fc78d7677525df1e9952ad33098.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3f022b18f3b30bccee515df5e47ff00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e92eac740953aa383be636ea90fd47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b941daa059b04aab552429ae22a1661d.png)
以上命题中正确命题的序号为
![](https://img.xkw.com/dksih/QBM/2017/9/1/1764924044869632/1766324751925248/STEM/fd072087f6394279acb2160612f289c2.png?resizew=108)
您最近一年使用:0次
解题方法
2 . 给出下列命题:
①如果平面
与平面
相交,那么它们只有有限个公共点;
②两个平面的交线可能是一条线段;
③经过空间任意三点的平面有且只有一个;
④如果两个平面有三个不共线的公共点,那么这两个平面就重合为一个平面.
其中正确命题的序号为________ .
①如果平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
②两个平面的交线可能是一条线段;
③经过空间任意三点的平面有且只有一个;
④如果两个平面有三个不共线的公共点,那么这两个平面就重合为一个平面.
其中正确命题的序号为
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解题方法
3 . 已知
,
表示两条不同的直线,
,
表示两个不同的平面,则下列四个命题中,所有正确命题的序号为____ .
① 若
,
,则
; ② 若
,
,则
;
③ 若
,
,则
; ④ 若
,
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
① 若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84b6e422b2e6f6dada4d8c369559a077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a042a14e1c3c915ad11544c9e1e57da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fe920cd78db25f5b4df37d066e57800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f747152f006301e03b643afb80195c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a042a14e1c3c915ad11544c9e1e57da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f4ded3c4bc7a2212f2a0eb5f9753de5.png)
③ 若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fe920cd78db25f5b4df37d066e57800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808c6d37467a5c995d71e49408503927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5986f2991d45fbf3578f08f27d9fd7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4042f9c51f83e3367d496e851735d7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a042a14e1c3c915ad11544c9e1e57da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a93a52c2b943e4c70ace99ed802d2b5.png)
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4 . 下列四个命题:
①样本相关系数r越大,线性相关关系越强;
②回归直线就是散点图中经过样本数据点最多的那条直线;
③设
是不同的直线,
是不同的平面,若
∥
,且
,
则
∥
且
∥
;
④若直线
不垂直于平面
,则直线
不可能垂直于平面
内的无数条直线.
其中正确命题的序号为
①样本相关系数r越大,线性相关关系越强;
②回归直线就是散点图中经过样本数据点最多的那条直线;
③设
![](https://img.xkw.com/dksih/QBM/2016/2/17/1572483885539328/1572483890921472/STEM/6f76625f7891461594cab492e98560d3.png)
![](https://img.xkw.com/dksih/QBM/2016/2/17/1572483885539328/1572483890921472/STEM/51187429bb184c8faebbe9375e8015aa.png)
![](https://img.xkw.com/dksih/QBM/2016/2/17/1572483885539328/1572483890921472/STEM/e918659909ff41f09f1964f3d1268fd2.png)
![](https://img.xkw.com/dksih/QBM/2016/2/17/1572483885539328/1572483890921472/STEM/50efb111160546b8afbbd771fb253724.png)
![](https://img.xkw.com/dksih/QBM/2016/2/17/1572483885539328/1572483890921472/STEM/a7ab2de4a38046aba3e0f3ba2df0f56a.png)
则
![](https://img.xkw.com/dksih/QBM/2016/2/17/1572483885539328/1572483890921472/STEM/70a5522db47a416987ecec1f392be2de.png)
![](https://img.xkw.com/dksih/QBM/2016/2/17/1572483885539328/1572483890921472/STEM/1d65d55792f84675b7c1a1bb75b8caec.png)
![](https://img.xkw.com/dksih/QBM/2016/2/17/1572483885539328/1572483890921472/STEM/70a5522db47a416987ecec1f392be2de.png)
![](https://img.xkw.com/dksih/QBM/2016/2/17/1572483885539328/1572483890921472/STEM/8479772fca5149bf889a7cb9174b5546.png)
④若直线
![](https://img.xkw.com/dksih/QBM/2016/2/17/1572483885539328/1572483890921472/STEM/50efb111160546b8afbbd771fb253724.png)
![](https://img.xkw.com/dksih/QBM/2016/2/17/1572483885539328/1572483890921472/STEM/1d65d55792f84675b7c1a1bb75b8caec.png)
![](https://img.xkw.com/dksih/QBM/2016/2/17/1572483885539328/1572483890921472/STEM/50efb111160546b8afbbd771fb253724.png)
![](https://img.xkw.com/dksih/QBM/2016/2/17/1572483885539328/1572483890921472/STEM/1d65d55792f84675b7c1a1bb75b8caec.png)
其中正确命题的序号为
A.①②③ | B.①③ | C.①②④ | D.③ |
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10-11高一下·辽宁大连·开学考试
5 . 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 |
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6 . 下列叙述中不正确的是________ .(填序号)
①如果两条直线都和第三条直线平行,那么这两条直线平行;②两条异面直线所成的角为锐角或直角;③直线
与
异面,
与
也异面,则直线
与
必异面.
①如果两条直线都和第三条直线平行,那么这两条直线平行;②两条异面直线所成的角为锐角或直角;③直线
![](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/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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7 . 已知命题:“若
,则
”为真命题,那么字母
在空间所表示的几何图形:①都是直线;
②都是平面;
③
是直线,
是平面;
④
是平面,
是直线.
其中正确结论的序号为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f04d04906af75cb9df8b9800d9b286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bd9fa99f51ca296c8f0ed6b9780adc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
②都是平面;
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e026ac41c5502a4743b336845bae2d95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
其中正确结论的序号为
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2010·江苏扬州·模拟预测
8 . 设
为使互不重合的平面,
是互不重合的直线,给出下列四个命题:
①![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f69cebb5302cf2f97d48d88e9d90854b.png)
②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8c7e0f62160264d889cb0329bc45c1c.png)
③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc33394c7a5b0ee1fdb70766f6ed11fd.png)
④若
;
其中正确命题的序号为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f69cebb5302cf2f97d48d88e9d90854b.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8c7e0f62160264d889cb0329bc45c1c.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc33394c7a5b0ee1fdb70766f6ed11fd.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ee1679158b5854fcd7ab68263f623a8.png)
其中正确命题的序号为
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11-12高三上·江苏泰州·期末
9 . 设
为互不重合的平面,
为互不重合的直线,给出下列四个命题:
①若
; ②若
∥
∥
,则
∥
;
③若
; ④若
.
其中正确命题的序号为_______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/725be6759947d258592cd888c4db4561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e5774d5b442de3e16992df33984dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95a454eb406d21dc2367ad24fc88f2ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ee1679158b5854fcd7ab68263f623a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c68b1bb92ca3e5a1cf5d32041db1c6.png)
其中正确命题的序号为
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10 . 连接球面上两点的线段称为球的弦,半径为4的球的两条弦AB、CD的长度分别为2
和4
,M、N分别是AB、CD的中点,两条弦的两端都在球面上运动,有下面四个命题:
①弦AB、CD可能相交于点M;
②弦AB、CD可能相交于点N;
③MN的最大值是5;
④MN的最小值是1;
其中所有正确命题的序号为_____ .
![](https://img.xkw.com/dksih/QBM/2016/3/9/1572527699361792/1572527705169920/STEM/da82dc25514f43a58e0bc73ed7ff01a9.png?resizew=20)
![](https://img.xkw.com/dksih/QBM/2016/3/9/1572527699361792/1572527705169920/STEM/2c8908502dbb4552a2a2739d991d4ebc.png?resizew=20)
①弦AB、CD可能相交于点M;
②弦AB、CD可能相交于点N;
③MN的最大值是5;
④MN的最小值是1;
其中所有正确命题的序号为
您最近一年使用:0次