1 . 如图,在长方体木料
中,
,
为棱
的中点.
(1)如图(1),求直线
与平面
所成角的正弦值.
(2)如图(2),要过点
和棱
将木料锯开.
①在木料表面画出符合要求的线,写出作图过程并说明理由;
②写出切割后体积较大的几何体的名称,并求出它的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f7ad41c55fab640a159a08a12c6b03c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/27/b7bbf9a1-e643-455c-b16b-d49c69a9b6b4.png?resizew=375)
(1)如图(1),求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb04914c4e8fb3483da44c67fe1809f.png)
(2)如图(2),要过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
①在木料表面画出符合要求的线,写出作图过程并说明理由;
②写出切割后体积较大的几何体的名称,并求出它的体积.
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解题方法
2 . 如图,在直三棱柱
中,
为
的中点,平面
过点
,
,
.
(1)作出
截直三棱柱
的截面,写出作图过程并说明理由;
(2)若
,
,求点
到截面的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/17/06f0ef54-2417-4148-9ea7-52f9b05e9881.png?resizew=170)
(1)作出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d355b4c58b4e883b9e65cc6da8622e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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名校
3 . 已知两个平面
,
,及两条直线
,
.则下列命题错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.若![]() ![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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2023-06-03更新
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6卷引用:福建省福州格致中学2022-2023学年高一下学期期末考试数学试题
福建省福州格致中学2022-2023学年高一下学期期末考试数学试题(已下线)专题04空间点、直线、平面的位置关系与空间直线、平面的平行-期末真题分类汇编(新高考专用)四川省成都市第七中学2023届高考热身文科数学试题四川省成都市第七中学2023届高考热身理科数学试题陕西省西安市第三中学2023-2024学年高三上学期期中数学(理科)试题宁夏银川一中、昆明一中2024届高三下学期联合考试二模文科数学试卷
4 . 如图所示,三棱台
中,
底面
,
.
![](https://img.xkw.com/dksih/QBM/2023/5/29/3248085625323520/3250092593766400/STEM/80584e2d5a434811b14a92871fd02199.png?resizew=180)
(1)证明:
是直角三角形;
(2)若
,问
为何值时,直线
与平面
所成角的正弦值为
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45378fbdfb5fe305c71893a91435854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed04b01505bbd8a4ac0bc12e46f23bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15faad881c8777c2f840cb89f1a8f849.png)
![](https://img.xkw.com/dksih/QBM/2023/5/29/3248085625323520/3250092593766400/STEM/80584e2d5a434811b14a92871fd02199.png?resizew=180)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7572ecc467c061ef71cf4486ec63ec3e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0583239d40db27f7c70325e1e7f54313.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73153657848013d2a1c3247d7f84ddeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041bac006360df1095a51b078765ef6d.png)
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解题方法
5 . 如图,在几何体
中,平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
平面
平面
,底面
为直角梯形.
为
的中点,
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/15/1d5a18c3-8fd0-45de-82bc-51a204c3ae9c.png?resizew=182)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc81d42ad20eb0b0ca0807e5a4c3ceb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e757f79f7d80369bb32cffe476c57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5a7cfed77121d5b0014c3487214fa59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/418b8c097da01831eb9efa8634689d26.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/15/1d5a18c3-8fd0-45de-82bc-51a204c3ae9c.png?resizew=182)
A.![]() | B.![]() |
C.![]() ![]() ![]() | D.几何体![]() |
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2023-05-13更新
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2卷引用:福建省三明市永安第九中学2022-2023学年高一下学期5月月考数学试题
解题方法
6 . 将边长为2的正方形纸片折成一个三棱锥,使三棱锥的四个面刚好可以组成该正方形纸片,若三棱锥的各顶点都在同一球面上,则该球的表面积为( )
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
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解题方法
7 . 在三棱锥P-ABC中,
,
,且
,
,
,
,则此三棱锥外接球的体积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c5383343e28ed187cc5e2b417e49bfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b60f7441172407b19e9e61b85a0170d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1f2ff0805c573e3c1fc1720d4e531e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-04-13更新
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1571次组卷
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7卷引用:福建省龙岩市连城县第一中学2023-2024学年高一下学期5月月考数学试题
福建省龙岩市连城县第一中学2023-2024学年高一下学期5月月考数学试题第13章《立体几何初步》单元达标高分突破必刷卷(基础版)-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(苏教版2019必修第二册)第13章 立体几何初步(B卷·能力提升)-【单元测试】2022-2023学年高一数学分层训练AB卷(苏教版2019必修第二册)广东省东莞市第七高级中学2022-2023学年高一下学期5月月考数学试题广西柳州高级中学、南宁市第三中学2023届高三联考数学(文)试题广西柳州高级中学、南宁市第三中学2023届高三联考数学(理)试题四川省广元中学2022-2023学年高二下学期期中数学试题(文科)
名校
8 . 如图,四棱锥
的底面是梯形,
,
,
,
,平面
平面
,
,
分别为线段
,
的中点,点
是底面
内
包括边界
的一个动点,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/14/684f1b4f-3880-49d4-9773-1ed7383f1317.png?resizew=188)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da2ebc3c7d1de745f52ae6908bebf3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce519312a849963b376c202c3f9d7cf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1328e05d150f86dbe18656662eaa8f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/14/684f1b4f-3880-49d4-9773-1ed7383f1317.png?resizew=188)
A.![]() |
B.三棱锥![]() ![]() |
C.异面直线![]() ![]() ![]() |
D.若直线![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-04-13更新
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1475次组卷
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7卷引用:福建省宁德市霞浦县2022-2023学年高一下学期期中数学试题
福建省宁德市霞浦县2022-2023学年高一下学期期中数学试题黑龙江省齐齐哈尔实验中学等校2022-2023学年高三下学期2月大联考数学试题湖南省长沙市长郡中学2024届高三上学期月考(二)数学试题江苏省镇江第一中学2023-2024学年高三上学期10月月考数学试题(已下线)广东省佛山市南海区桂城中学2024届高三上学期11月月考数学试题(已下线)湖南省长沙市长郡中学2024届高三上学期月考(二)数学试题变式题11-14江苏省2024届高三上学期期末迎考数学试题
解题方法
9 . 如图,在四棱锥
中,底面
为矩形,
平面
,
,
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/6/07855c7d-24eb-4423-8e07-beee009bd930.png?resizew=166)
(1)证明:
平面
.
(2)证明:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f6967901d6c855864df01e7bf7a15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/6/07855c7d-24eb-4423-8e07-beee009bd930.png?resizew=166)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2023-04-05更新
|
836次组卷
|
6卷引用:福建省福州福清市2017-2018学年学年高一上学期期末考试数学试题
21-22高一下·福建·期中
名校
10 . 如图,在三棱锥
中,
和
均是边长为6的等边三角形,P是棱
上的点,
,过点P的平面
与直线
垂直,且平面
平面
.过直线l及点C的平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/3/aa110b0c-8325-43fa-8b00-1be7821a8028.png?resizew=182)
(1)在图中画出l,写出画法(不必说明理由);
(2)求证:
;
(3)若直线
与平面
所成角的大小为
,求平面
与平面
所成的锐二面角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a94d59dee2d5a8f0425b64b2083825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f63075fdeeb9e765dd696c4ff43ba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4fce8e923062b9779553d6f282895b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1319a44dc601303876d3dab3372660.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a392d05d3cfcbb438569b1ea9980dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/670684ed4962fcebce7b5a140510d066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/863dd235346ce076540230e8eb4122f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/138ca330a165c68e865cacd35c18a665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec6c3f8d8a0611bf49e269bd288949d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/3/aa110b0c-8325-43fa-8b00-1be7821a8028.png?resizew=182)
(1)在图中画出l,写出画法(不必说明理由);
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23a63f6aa604e3d7fc7ae8c7b587069a.png)
(3)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a392d05d3cfcbb438569b1ea9980dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1902d864d3f16535e273f7851b92a4fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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