名校
解题方法
1 . 已知四棱锥
的底面
是矩形,
底面
,点
、
分别是棱
、
的中点,则①棱
与
所在直线垂直:②平面
与平面
垂直;③
的面积大于
的面积;④直线
与直线
是异面直线.以上结论正确的个数为___________ 个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76a935359a3c5113c218edd0d0ce5dcb.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
您最近一年使用:0次
2021-08-25更新
|
313次组卷
|
10卷引用:山西省昌梁市贺昌中学2020-2021学年高二上学期期中数学试题
山西省昌梁市贺昌中学2020-2021学年高二上学期期中数学试题人教A版2017-2018学年必修二第2章 章末综合测评1数学试题2018届高考数学高考复习指导大二轮专题复习:专题五 立体几何 测试题5智能测评与辅导[文]-立体几何的综合问题江西省宜春市第二中2019-2020学年高二上学期期末数学(文)试题山西省山西大学附属中学2018-2019学年高二上学期期中数学(理)试题山西省山西大学附属中学2018-2019学年高二上学期期中数学(文)试题广西玉林市第十一中学2020-2021学年高一4月期中数学试题河北省张家口市第一中学(普通实验班)2020-2021学年高二上学期10月月考数学试题(已下线)考点32 异面直线所成的角-备战2022年高考数学典型试题解读与变式
12-13高二上·湖北武汉·期中
名校
2 . 在三棱锥
中,
平面
,垂足为
,且
,则点
一定是
的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30fc65a72853bd8ac1ad0828270d3baf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.内心 | B.外心 | C.重心 | D.垂心 |
您最近一年使用:0次
2021-08-07更新
|
946次组卷
|
12卷引用:【校级联考】山西省吕梁市泰化中学2018-2019学年高二上学期第一次月考数学试卷
【校级联考】山西省吕梁市泰化中学2018-2019学年高二上学期第一次月考数学试卷(已下线)2011-2012学年湖北省武汉市部分重点中学高二上学期期中数学试卷2015-2016学年甘肃省天水市秦安县一中高一上学期期末考试数学试卷山西省太原市2020-2021学年高一下学期期末数学试题重庆市荣昌中学校2020-2021学年高二上学期十月月考数学试题江西省吉安市(吉安县三中、泰和二中、安福二中、井大附中)2021-2022学年高二上学期联考数学(理)试题(已下线)第13课时 课中 直线与平面垂直的性质江西省南昌市第十中学2021-2022学年高二下学期第一次月考数学(文)试题江西省南昌市第十中学2021-2022学年高二下学期第一次月考数学(理)试题6.5.1直线与平面垂直的性质 课时练习2020-2021学年高一下学期数学北师大版(2019)必修第二册湖南省岳阳市平江县第三中学2023-2024学年高二普通高中学业水平合格性考试仿真模拟(专家卷四)数学试题安徽省合肥市第一中学2023-2024学年高二下学期学业水平考试数学模拟卷
解题方法
3 . 已知直三棱柱
中,侧面
为正方形.
,
,
,
分别为
和
的中点.
![](https://img.xkw.com/dksih/QBM/2021/7/7/2759308540600320/2777762141732864/STEM/64f56226758a4e4ebdaf97d3e2d28385.png?resizew=177)
(1)求三棱锥
的体积;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae341f580ff8fbf21f616fe900b0e4b9.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://img.xkw.com/dksih/QBM/2021/7/7/2759308540600320/2777762141732864/STEM/64f56226758a4e4ebdaf97d3e2d28385.png?resizew=177)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/437c9774700f6c066b3e19d17d54b368.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64834e6560efa2fc81651c2a1cea3e7f.png)
您最近一年使用:0次
解题方法
4 . 如图,正方体
的棱长为1,线段
上有两个动点
,
(
靠近
),且
,则下列结论中正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/12/c26ac40d-99dc-41c2-9a42-b62d0162eb52.png?resizew=181)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f115f2683c0422042f1846450885e7fe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/12/c26ac40d-99dc-41c2-9a42-b62d0162eb52.png?resizew=181)
A.![]() |
B.存在点![]() ![]() ![]() ![]() |
C.三棱锥![]() |
D.![]() ![]() |
您最近一年使用:0次
名校
5 . 如图,在直三棱柱
中,底面
是边长为3的等边三角形,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2021/5/12/2719393870585856/2722325121474560/STEM/027f29b0-d037-4eb9-9853-33f2bd3c4c59.png?resizew=161)
(Ⅰ)证明:
;
(Ⅱ)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/418b7d3ed7be669fb165da9b164e468b.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/2021/5/12/2719393870585856/2722325121474560/STEM/027f29b0-d037-4eb9-9853-33f2bd3c4c59.png?resizew=161)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/148a7179643fbfca370172f99d7acd94.png)
(Ⅱ)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d064ea932f0858ea6dfb06f523bc0f8a.png)
您最近一年使用:0次
2021-05-16更新
|
930次组卷
|
2卷引用:山西省吕梁市2021届高三三模数学(文)试题
解题方法
6 . 如图所示的三棱锥
,
平面
,
,若
,
,
,
,当
取最大值时,点
到平面
的距离为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/9188119f-5fad-47e6-b6e2-e128bdf66e15.png?resizew=125)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c4340dcffb0783d118a587e5352a2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00803e67a5d417a9a4dc00277fca778b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c884a45b56bc34d79273b067c1520b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a54bf739ada87edb51304d38f09b46d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba03505a2ec6653c4a65830d61694c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f384e98d574fa2676d61624285f88188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/9188119f-5fad-47e6-b6e2-e128bdf66e15.png?resizew=125)
A.![]() | B.![]() | C.![]() | D.5 |
您最近一年使用:0次
2021-05-16更新
|
1390次组卷
|
6卷引用:山西省吕梁市2021届高三三模数学(文)试题
山西省吕梁市2021届高三三模数学(文)试题陕西省2021届高三下学期教学质量检测测评(五)文科数学试题(已下线)“超级全能生”2021届高三全国卷地区5月联考试题(乙卷)数学(文)试题(已下线)“超级全能生”2021届高三全国卷地区5月联考试题(甲卷)数学(文)试题(已下线)考点17 基本不等式-备战2022年高考数学(文)一轮复习考点微专题(已下线)专题18 立体几何空间距离与截面100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)
7 . 如图,四棱锥
中,
,
,侧面
为等边三角形,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/270a68e3-be52-4cf0-b44c-7d6d8d38eae6.png?resizew=155)
(1)求证:
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6a2b112facda441f4e34bf5c145fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba74c764e89336077603ec941e7b5282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b29be7e805ababb37bbc7d7f894e21f0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/270a68e3-be52-4cf0-b44c-7d6d8d38eae6.png?resizew=155)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9971233dc3e8ef828046fbb94101b9d0.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ab58222b40ffaf2dd6a66a81806e7c.png)
您最近一年使用:0次
8 . 已知四棱锥
中,底面
是矩形,侧面
是正三角形,且侧面
底面
,
,若四棱锥
外接球的体积为
,则该四棱锥的表面积为( )
![](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/852aabd89edffc1b94344ff3f1f31ccd.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/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccbd93442fc3e73c97d6d54f01d6cd1d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-02-07更新
|
1167次组卷
|
6卷引用:山西省吕梁市2021届高三上学期第一次模拟数学(理)试题
山西省吕梁市2021届高三上学期第一次模拟数学(理)试题(已下线)专题09 立体几何(讲)-2021年高考数学二轮复习讲练测(文理通用)(理科)(已下线)专题09 立体几何(讲)-2021年高考数学二轮复习讲练测(文科)(文理通用)(已下线) 专题22 几何体的表面积与体积的求解 (讲)-2021年高三数学二轮复习讲练测(文理通用)(已下线) 专题18 几何体的表面积与体积的求解 (讲)-2021年高三数学二轮复习讲练测(新高考版)(已下线)专题21几何体与球切、接的问题(测)- 2021年高三数学二轮复习讲练测 (文理通用)
解题方法
9 . 如图,四棱锥P-ABCD中,底面ABCD为平行四边形,
,
,
底面ABCD.
![](https://img.xkw.com/dksih/QBM/2021/1/23/2642346579034112/2644386019434496/STEM/c893fbd0-b506-4b15-9bb8-963ced0dc35a.png)
(1)证明:
;
(2)设
,过BD的平面交PC于点M,若
,求三棱锥P-AMD的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e0b64d25ddd18454f88e40c45d7d8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c4e4a162f12d12a082b8d8fdd1aeab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://img.xkw.com/dksih/QBM/2021/1/23/2642346579034112/2644386019434496/STEM/c893fbd0-b506-4b15-9bb8-963ced0dc35a.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b07e317ffe7859e81b42ef4970e344a.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b624742fe28db114e0554c6c87bff05c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c21a72b548b71edd220999255ca5043.png)
您最近一年使用:0次
2021-01-26更新
|
66次组卷
|
3卷引用:山西省吕梁市2020-2021学年高二上学期期末数学(文)试题
10 . 如图,
,
平面ABC,则在
和
的边所在的直线中,与AP垂直的直线是_______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3cc9cccfb4c260dac05f4ed57e8c10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
![](https://img.xkw.com/dksih/QBM/2021/1/23/2642332216942592/2643197503750144/STEM/3724ed61-e213-4c43-bb47-0ef2eed53dc2.png?resizew=234)
您最近一年使用:0次
2021-01-24更新
|
80次组卷
|
2卷引用:山西省吕梁市2020-2021学年高二上学期期末数学(理)试题