1 . 如图,已知四边形
为梯形,
,
,四边形
为矩形,且平面
平面
,又
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/be665de8-fb59-4a20-b430-4866e2743145.png?resizew=188)
(1)求证:
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be4e903f726661da71895b03e982a5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbc56d42b003cbcb1fbe5c50e55b26b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c0db1f4f666a9be9ede868065a50997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f23bfbec3f97a797706e87a2d5a5938.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dbe4a746261639d50bb430620e4e3a7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/be665de8-fb59-4a20-b430-4866e2743145.png?resizew=188)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/408c0583576eb52299048703e3125367.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
您最近一年使用:0次
2019-12-16更新
|
362次组卷
|
2卷引用:2019年11月中学生标准学术能力诊断性测试测试文科数学试题(一卷)
2 . 如图,在长方体
中,
,
,点
在棱
上移动.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/ebb5f72f-1daf-45c9-a863-4325b2cff680.png?resizew=193)
(1)证明:
;
(2)求直线
与平面
所成的角;
(3)当
为
的中点时,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7d64fc81c857b124268609a8beb77b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/ebb5f72f-1daf-45c9-a863-4325b2cff680.png?resizew=193)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0fa81c1f81266b4ef3d471bc6bfc38d.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11990928efcd42ebe7a82a5f1105a708.png)
您最近一年使用:0次
2019-12-01更新
|
445次组卷
|
2卷引用:江苏省扬州市邗江中学2019-2020学年高一上学期期中数学试题(新疆班)
名校
3 . 如图,在三棱锥
中,平面
平面
,
为等边三角形,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/89a56215-dea8-4ad9-a5bd-973f4ff03dc6.png?resizew=220)
(1)证明:
;
(2)若
,求二面角
平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ab13ef156d034b710d811e09b0be34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/89a56215-dea8-4ad9-a5bd-973f4ff03dc6.png?resizew=220)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4cd8ba7eb52e38857830162e770f534.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87aed767c861502aff771e6b0114746c.png)
您最近一年使用:0次
2019-11-21更新
|
2370次组卷
|
8卷引用:2019年11月四川省攀枝花市一模数学(理)试题
4 . 如图,菱形
所在平面与
所在平面垂直,且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/eb560bfc-270e-4988-83c3-b6943182c5e0.png?resizew=185)
(1)求证:
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3814287dbb60d478bffc5366f9928b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/130e684c831039a1e49c7f7f554959bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9e8e717cd627ae77de4f589c163f2bf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/eb560bfc-270e-4988-83c3-b6943182c5e0.png?resizew=185)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b4424cb0af429b92e1fc168c4c70de4.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
您最近一年使用:0次
2019-11-21更新
|
420次组卷
|
2卷引用:广东省2019-2020学年高三第一次教学质量检测理科数学试题
名校
5 . 正方体
中,直线
与平面
所成的角的大小为________ (结果用反三角函数值表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
您最近一年使用:0次
2019-11-09更新
|
295次组卷
|
3卷引用:上海市金山中学2018-2019学年高二下学期3月月考数学试题
上海市金山中学2018-2019学年高二下学期3月月考数学试题(已下线)上海市金山中学2019-2020学年高二上学期月考数学试题上海市浦东新区南汇中学2021-2022学年高二上学期10月月考数学试题
名校
6 . 如图,在四棱锥
中,底面
是正方形,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/3c3a875b-b1de-45b0-88a3-9c6d5a7ef5a8.png?resizew=216)
(1)证明:
平面
;
(2)若
是
的中点,
是棱
上一点,且
平面
,求二面角
的余弦值.
![](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/0e7b6d04f024ca05cdfacc8ce9137c15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ce2e773ee3f553baf5d56582c6ade1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/3c3a875b-b1de-45b0-88a3-9c6d5a7ef5a8.png?resizew=216)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c372d059202ec388960b125d4a87dc84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734735213b599a9915e1ed91a5d8ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281177cc5c7e6294a474dc64ee02aa29.png)
您最近一年使用:0次
2019-11-06更新
|
1394次组卷
|
2卷引用:2019年贵州省铜仁市铜仁第一中学三模数学(理)试题
名校
7 . 在空间四边形ABCD中,
,
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a651eb577dbada1f29590e558d6f9fa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc1f76257275ab4b04f9bc913535670.png)
您最近一年使用:0次
2019-10-10更新
|
67次组卷
|
2卷引用:宁夏银川市育才中学学益校区2019-2020学年高一上学期第二次月考数学试题
名校
8 . 如图
,在梯形
中,
,
,
为
的中点,
是
与
的交点,将
沿
翻折到图
中
的位置,得到四棱锥
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/1479b53f-bec0-4f63-b572-9e04d3b5b352.png?resizew=420)
(1)求证:
;
(2)当
,
时,求
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4299cca48ff6abfb252ef73b5e62317d.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3814287dbb60d478bffc5366f9928b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b04e2f190be01e1ae0a21eb44e4dce83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db2b1c641b93caae9b7a82441e4ba70.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/1479b53f-bec0-4f63-b572-9e04d3b5b352.png?resizew=420)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed2a23c5569ecf4ab6ccf927a4ab46f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/783a833992e0862211a15fec2d3e3dda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7470868b0a5dc869acc97e586cb06477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eddaf3f33bd9a99162c061c9dd99aee.png)
您最近一年使用:0次
2019-09-19更新
|
1020次组卷
|
4卷引用:广东省广雅中学、执信、六中、深外四校2020届高三8月开学联考数学文试题
广东省广雅中学、执信、六中、深外四校2020届高三8月开学联考数学文试题江西省临川第一中学2019-2020学年高三上学期10月月考数学(文)试题(已下线)专题8.8 第八章 空间向量与立体几何(单元测试)(测)-浙江版《2020年高考一轮复习讲练测》广东省执信中学2019-2020学年高二上学期9月月考数学试题
名校
9 . 把平面图形
上的所有点在一个平面上的射影构成的图形
称为图形
在这个平面上的射影.如图,在长方体
中,
,
,
.则
在平面
上的射影的面积是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da895d8bd043625a0839128252130d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a0c3a4e61b97fa9bc58f3179fc2958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86338536656046e93b53672ade9a78b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69c2e70f28845c57f004b64f6fe46573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8257b6bd25104e07b9ad935c0a3aac4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/033aae04-e289-4932-8ceb-b9bf9cf072c6.png?resizew=155)
您最近一年使用:0次
名校
10 . 在正方体
中,点
是四边形
的中心,关于直线
,下列说法正确的是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc526324e78e4d9226d1b537f27845a.png)
A.![]() | B.![]() |
C.![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
2019-09-19更新
|
1825次组卷
|
12卷引用:【市级联考】广东省汕头市2019年普通高考第一次模拟考试数学理试题
【市级联考】广东省汕头市2019年普通高考第一次模拟考试数学理试题【市级联考】广东省汕头市2019届高三第一次模拟考试文科数学试题新疆伊犁哈萨克自治州奎屯市第一高级中学2018-2019学年高二下学期第二次月考数学(理)试题天津市和平区第一中学2018-2019学年高一下学期期中数学试题1广东省广雅中学、执信、六中、深外四校2020届高三8月开学联考数学文试题天津市和平区第一中学2018-2019学年高一下学期期中数学试题2(已下线)专题8.3 空间点、直线、平面之间的位置关系(练)-浙江版《2020年高考一轮复习讲练测》河南省濮阳市2019-2020学年高一上学期期末数学试题2020届广东省佛山市禅城区高三上学期统一调研测试(二)数学(文)试题(已下线)专题24 平行与垂直的判定与性质-冲刺2020高考跳出题海之高三数学模拟试题精中选萃新疆昌吉市第九中学2021届高三上学期开学考试数学(理)试题(已下线)专题8.3 空间点、直线、平面之间的位置关系(练)-2021年新高考数学一轮复习讲练测