名校
解题方法
1 . 如图,在棱长为1的正方体中,点P是线段
上一动点(不与
,B重合),则下列命题中:
①平面
平面
;
②
一定是锐角;
③
;
④三棱锥
的体积为定值.
其中真命题的有__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
①平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c1baaa912fedaaf6670730bfad1de32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf74a5f57a377b91ea36680e2c6b4815.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc6913da03b6e87d163d17c1dc34295c.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7fe8889c7ac022128a40c633282de4b.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/894fcea66eb492bec09c11f106b9b4fa.png)
其中真命题的有
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/21/24b3c10a-18cc-45ac-a8c9-fc9c5d43ed0e.png?resizew=152)
您最近一年使用:0次
2023-03-20更新
|
1406次组卷
|
7卷引用:河南省开封市通许县2023届高三三模文科数学试题A卷
2 . 已知长方体
的棱
,
,点
,
分别为棱
,
上的动点.若四面体
的四个面都是直角三角形,则下列命题正确的是__________ .(写出所有正确命题的编号)
①存在点
,使得
;
②不存在点
,使得
;
③当点
为
中点时,满足条件的点
有3个;
④当点
为
中点时,满足条件的点
有3个;
⑤四面体
四个面所在平面,有4对相互垂直.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/557a1bc648125cc09cb63412bc13ea1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a0ecba7e1969a265ff75bcb17ed9d2e.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/458d492ab8896be57a54ec905d8e2f4f.png)
①存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48fb4d62850da19eaa4b793b6f75effc.png)
②不存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc61562565dcbaa1bbeec6a307634c0b.png)
③当点
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
④当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
⑤四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/458d492ab8896be57a54ec905d8e2f4f.png)
您最近一年使用:0次
2020-08-15更新
|
1313次组卷
|
4卷引用:河南省焦作市温县第一高级中学2021-2022学年高二上学期11月月考文科数学试题
河南省焦作市温县第一高级中学2021-2022学年高二上学期11月月考文科数学试题安徽省合肥市2020届高三下学期第三次教学质量检测数学(文)试题安徽省阜阳市太和第一中学2020-2021学年高二上学期12月月考理科数学(奥赛班)试题(已下线)黄金卷14-【赢在高考·黄金20卷】备战2021高考数学全真模拟卷(新高考专用)
2010·浙江嘉兴·一模
名校
解题方法
3 . 如图所示,在正方体
中,
分别是棱
、
的中点,
的顶点P在棱
与棱
上运动,有以下四个命题:
![](https://img.xkw.com/dksih/QBM/2020/11/9/2589447185227776/2591149047930880/STEM/3d27731cf5514d0bbec214c30598fa3b.png?resizew=178)
(1)平面
;
(2)平面
⊥平面
;
(3)
在底面
上的射影图形的面积为定值;
(4)
在侧面
上的射影图形是三角形.
其中正确命题的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deec8447b2ed46fd7b3414b8fb9830bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://img.xkw.com/dksih/QBM/2020/11/9/2589447185227776/2591149047930880/STEM/3d27731cf5514d0bbec214c30598fa3b.png?resizew=178)
(1)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1ce27cc099d81d330333186a62b2a8.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35bf3027652cb34dcf0f56f93b61320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09104d630957bf95bda31af7499ad0cb.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deec8447b2ed46fd7b3414b8fb9830bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deec8447b2ed46fd7b3414b8fb9830bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538b539984b64f0626bdb2195cc3068b.png)
其中正确命题的序号是
您最近一年使用:0次
2020-11-12更新
|
1330次组卷
|
14卷引用:河南省重点高中2021-2022学年高二上学期阶段性调研联考一文科数学试题
河南省重点高中2021-2022学年高二上学期阶段性调研联考一文科数学试题(已下线)2010年高考嘉兴一中适应性考试数学试题(理科)上海市浦东新区2017-2018学年第一学期高三数学期中质量检测试卷辽宁省六校协作体2017-2018学年高一下学期开学考试数学试题山西省山西大学附属中学校2019-2020学年高二上学期期中数学(理)试题山西省大学附属中学校2019-2020学年高二上学期期中数学(文)试题江西省奉新县第一中学2020-2021学年高二上学期第二次月考数学(文)试题山西省山西大学附属中学、汾阳中学2020-2021学年高二上学期12月月考数学(理)试题山西省山西大学附属中学、汾阳中学2020-2021学年高二上学期12月月考数学(文)试题(已下线)第33练 立体几何的综合-2021年高考数学(文)一轮复习小题必刷(已下线)第31练 直线、平面垂直的判定与性质-2021年高考数学(文)一轮复习小题必刷(已下线)专题07 平行与垂直的证明-备战2021年高考数学二轮复习题型专练(新高考专用)陕西省西安市第三中学2020-2021学年高一上学期第三次诊断性测试数学试题(已下线)课时42 空间平面与平面的位置关系-2022年高考数学一轮复习小题多维练(上海专用)
4 . 如图,在梯形
中,
,
,
,
分别是
的中点,将四边形
沿直线
进行翻折.给出四个结论:①
;②
;③平面
平面
;④平面
平面
.在翻折过程中,可能成立的结论序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4275a32ff9031b2ffc61e078a9b766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28d2790a97390935125aa897417f970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08c14e87a2bcf7090eab2fea73667d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d276d0010fd458383ea3dd61415e1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db1cb818977a967130ef41cd3f9f4fc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15f3e3f310f6ec3f3a26498e7ee17a00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f1d7219cd40346442b33dba84deb5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b189e0bf776fc95971e2ef60cdfc454e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f1d7219cd40346442b33dba84deb5c.png)
![](https://img.xkw.com/dksih/QBM/2018/2/23/1888433483808768/1891511787331584/STEM/83e5fbfb6db54584bcc0ce6f1ac16bc5.png?resizew=131)
您最近一年使用:0次
2018-02-27更新
|
536次组卷
|
5卷引用:【市级联考】河南省濮阳市2018-2019学年高一上学期期末考试数学试题
【市级联考】河南省濮阳市2018-2019学年高一上学期期末考试数学试题四川省乐山市2017-2018学年高二上学期期末教学质量检测数学理试题四川省乐山市2017-2018学年高二上学期期末教学质量检测数学(文)试题(已下线)专题8.6 立体几何 (单元测试)(测)【文】-《2020年高考一轮复习讲练测》(已下线)专题8.6 立体几何(单元测试)(测)-江苏版《2020年高考一轮复习讲练测》
名校
解题方法
5 . 如图所示,正方体
的棱长为
,
、
分别是棱
、
的中点,过直线
的平面分别与棱
、
交于
、
,设
,
,给出以下四个命题:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/9/4fc639e4-ab43-4dc5-9760-bc06edb392a4.png?resizew=211)
①平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e92eac740953aa383be636ea90fd47.png)
平面
;
②当且仅当
时,四边形
的面积最小;
③四边形
周长
,
是单调函数;
④四棱锥
的体积
为常函数;
以上命题中真命题的序号为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.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/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ecac2dad4cffdd971fd23deacff3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b25f3ea33cc08b1e2a0d9c3a9dccaf.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/75f51cd1e351fac1c7c6006aac6bda5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/9/4fc639e4-ab43-4dc5-9760-bc06edb392a4.png?resizew=211)
①平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e92eac740953aa383be636ea90fd47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbfc21c182d284d0a028210baa4dea49.png)
②当且仅当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a35adc3571a6e5c8dd9a8fb51315ee6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e92eac740953aa383be636ea90fd47.png)
③四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e92eac740953aa383be636ea90fd47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ba045bdc35e3e880653fca61265a1e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
④四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf43f974932cc0d83c0e898a4f00a72b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f1dd907172fa422e8845d0bb35b7176.png)
以上命题中真命题的序号为
您最近一年使用:0次
2016-12-04更新
|
479次组卷
|
3卷引用:2015-2016学年河南省信阳高中高一下学期开学考试数学卷