名校
1 . 如图,在三棱柱
中,
分别为
的中点,则下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c2d86d8daea5e652d99fe1c6bc3f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c21840e2f00fe67676dd3a90a40dd3a.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-04-06更新
|
3452次组卷
|
10卷引用:四川省成都市成华区某校2023-2024学年高三“三诊”数学(文)试题
四川省成都市成华区某校2023-2024学年高三“三诊”数学(文)试题湖南省新高考教学教研联盟2024届高三下学期第二次联考数学试题广东省茂名市高2024届高三下学期高考模拟数学试题(已下线)8.4.1 平面【第三课】“上好三节课,做好三套题“高中数学素养晋级之路福建省三明第一中学2023-2024学年高一下学期期中考试数学试卷海南省海南中学2023-2024学年高一下学期期中考试数学试题黑龙江省大庆市实验中学实验二部2023-2024学年高三下学期阶段考试数学试题河南省信阳高级中学2023-2024学年高一下学期5月期中考试数学试题(已下线)第8.4.1讲 平面-同步精讲精练宝典(人教A版2019必修第二册)湖北省荆州市荆州中学2023-2024学年高一下学期5月月考数学试卷
名校
解题方法
2 . 如图,四棱锥
的底面是矩形,PA⊥底面ABCD,
,
,M,N分别为CD,PD的中点,K为PA上一点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/36dc1423-0da9-4eac-9718-9d3739db7b90.png?resizew=160)
(1)证明:B,M,N,K四点共面;
(2)若PC与平面ABCD所成的角为
,求平面BMNK与平面PAD所成的锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c406e7d1e7977dd5b30ef81cfdc8e8d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267ace52b64e1e7dfc5211e033255b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f79ca4a12066237fd4eba14dba3e24.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/36dc1423-0da9-4eac-9718-9d3739db7b90.png?resizew=160)
(1)证明:B,M,N,K四点共面;
(2)若PC与平面ABCD所成的角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3427311203b1958b9ff89084c66a09a.png)
您最近一年使用:0次
2023-02-19更新
|
895次组卷
|
5卷引用:四川省阆中中学校2023届高三全景模拟卷(一)理科数学试题
四川省阆中中学校2023届高三全景模拟卷(一)理科数学试题贵州省毕节市2023届高三年级诊断性考试(一)数学(理)试题四川省南充高级中学2022-2023学年高三下学期第九次月考数学理科试题(已下线)专题14立体几何(解答题)(已下线)专题19 空间几何解答题(理科)-3
3 . 在棱长为2的正方体
中,已知点P为棱
的中点,点Q为棱CD上一动点,底面正方形ABCD内的点M始终在平面
上,则由所有满足条件的点M构成的区域的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a019240236421a56d33ed143b476154.png)
您最近一年使用:0次
4 . 如图,在棱长为2的正方体
中,E,F,G,H分别是所在棱的中点.
![](https://img.xkw.com/dksih/QBM/2022/3/18/2939013715066880/2939679107670016/STEM/6ac8f825b56e4257aba7db856deea5a0.png?resizew=170)
(1)求证:E,F,G,H四点共面;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/2022/3/18/2939013715066880/2939679107670016/STEM/6ac8f825b56e4257aba7db856deea5a0.png?resizew=170)
(1)求证:E,F,G,H四点共面;
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2150493985097f1c23e10a3f553d0e5.png)
您最近一年使用:0次
解题方法
5 . 已知空间几何体ABCDE中,
,
是全等的正三角形,平面
平面BCD,平面
平面BCD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/fd2165e6-a2e8-48ee-9b56-ecbb088e06ce.png?resizew=158)
(1)若
,求证:
;
(2)探索A,B,D,E四点是否共面?若共面,请给出证明;若不共面,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b265d121f9ebc13671a5719604476a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7fb4bb4caccf79639a126064771da5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/fd2165e6-a2e8-48ee-9b56-ecbb088e06ce.png?resizew=158)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7206d0c258d2bbae8a667b2803d0804a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/706208480fe1cd60cb1d93f27b51accc.png)
(2)探索A,B,D,E四点是否共面?若共面,请给出证明;若不共面,请说明理由.
您最近一年使用:0次
6 . 如图,已知四边形
和
均为直角梯形,
,
且
,平面
平面
,
.
![](https://img.xkw.com/dksih/QBM/2017/1/19/1619466238443520/1619466239090688/STEM/f2541006f3b4496786f409f1c2468620.png)
(1)求证:
平面
;
(2)求平面
和平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/693cd6179b2a92f03153ce12a0e86b95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cc3c947dc4deaf4eb5266772e43bee0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1057fba69b1554ceff580f73dbb28ff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/693cd6179b2a92f03153ce12a0e86b95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502fda7d60b3aa884b23094fac16ab63.png)
![](https://img.xkw.com/dksih/QBM/2017/1/19/1619466238443520/1619466239090688/STEM/f2541006f3b4496786f409f1c2468620.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e2fef2c0e49ecae8688ca60802310e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
您最近一年使用:0次
7 . 如图,在四棱锥
中,底面
为直角梯形,
,
底面
,
,
为
的中点,
为棱
的中点.
![](https://img.xkw.com/dksih/QBM/2016/9/8/1573007093145600/1573007099224064/STEM/d180af331854481bba52a4ea298e7db0.png)
(1)证明:
平面
;
(2)已知
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6153163fecdf3f410411048428ccaef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083201b6b527a852ff51831bd71c99cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e458f4503e211b542f6f30c8a34eaca5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57cdaf395942435e770920e0cf62605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2016/9/8/1573007093145600/1573007099224064/STEM/d180af331854481bba52a4ea298e7db0.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df22ab3b1b32ff5e07407c133ed1bdcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c233190f9339e777fe26c7b690541baf.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e159921cdcf0e3bb64ddc32015e1a361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c233190f9339e777fe26c7b690541baf.png)
您最近一年使用:0次
8 . 四棱锥S-ABCD中,侧面SAD是正三角形,底面ABCD是正方形,且平面SAD⊥平面ABCD,M、N分别是AB、SC的中点.
(Ⅰ)求证:MN∥平面SAD;
(Ⅱ)求二面角S-CM-D的余弦值.
(Ⅰ)求证:MN∥平面SAD;
(Ⅱ)求二面角S-CM-D的余弦值.
您最近一年使用:0次
9 . 如图,
为正三角形,
平面
,
,
为
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/2015/2/10/1571988166696960/1571988172652544/STEM/7ceeca21c96e482ca28e086c28fac2fd.png)
(Ⅰ)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
平面
;
(Ⅱ)求平面
与平面
所成的锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19efd943fe98bcea0394795a7bc06f33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/082f4777d26f09734bfa559e064038fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1642eec556eb252de9c1ab7bb5ca90b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afc09970c72e7921f392bdac2b51fcce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb08f6a798dc293f3d8de281190f65e.png)
![](https://img.xkw.com/dksih/QBM/2015/2/10/1571988166696960/1571988172652544/STEM/7ceeca21c96e482ca28e086c28fac2fd.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(Ⅱ)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823f4e614dd9290178c2b9c9fd2460a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
10 . 已知
是平面,
是直线,则下列命题正确的是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d1a34ae2b8c77f8d7e355c6d1d667e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次