名校
解题方法
1 . 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)
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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
2 . 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
3 . 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.
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4 . 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)
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5 . 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
6 . 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
7 . 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
8 . 如图,在四棱锥P—ABCD中,底面ABCD是边长为4的菱形,且
,菱形ABCD的两条对角线的交点为0,PA=PC,PB=PD,且PO=3.点E是线段PA的中点,连接EO、EB、EC.
![](https://img.xkw.com/dksih/QBM/2012/5/10/1570852891713536/1570852897185792/STEM/f0e02adcc29e4680a3b50e130d347db8.png)
(I)证明:直线OE//平面PBC;
(II)求二面角E-BC-D的大小
![](https://img.xkw.com/dksih/QBM/2012/5/10/1570852891713536/1570852897185792/STEM/7a8ca84c69aa49f691c019f6807feb05.png)
![](https://img.xkw.com/dksih/QBM/2012/5/10/1570852891713536/1570852897185792/STEM/f0e02adcc29e4680a3b50e130d347db8.png)
(I)证明:直线OE//平面PBC;
(II)求二面角E-BC-D的大小
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