解题方法
1 . 如图,在四棱锥P-ABCD中,
,
,
,
, PA=AB=BC=2. E是PC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/10/4a437dc6-bc09-4e3f-8941-89fcbe63e6dd.png?resizew=139)
(1)证明:
;
(2)求三棱锥P-ABC的体积;
(3) 证明:
平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbb05b8b630052ff544249ebd72d95d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db27b7f29d7d01b2692f217bc3079fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf10d92f20501e19d25f6f4159aab89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38cffa0b9b2cf2e5a0f4e2832046815.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/10/4a437dc6-bc09-4e3f-8941-89fcbe63e6dd.png?resizew=139)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44f4120c94cb7176dc31fcac387b32e.png)
(2)求三棱锥P-ABC的体积;
(3) 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
名校
解题方法
2 . 如图,在四棱锥
中,
,
,平面
底面
,
,
和
分别是
和
的中点,求证:
![](https://img.xkw.com/dksih/QBM/2020/2/17/2401128498978816/2401658692321280/STEM/dddfbd4f30a641f1a8f8f78663ca3a3c.png?resizew=113)
(1)
底面
;
(2)平面
平面
;
(3)平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d551df565f796c9397598bbd6789ed.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/db27b7f29d7d01b2692f217bc3079fc4.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2020/2/17/2401128498978816/2401658692321280/STEM/dddfbd4f30a641f1a8f8f78663ca3a3c.png?resizew=113)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b00939b2343fcd50041d79b75156b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(3)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51838e395dfc9d9ef597d9e01f46272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2020-02-18更新
|
322次组卷
|
7卷引用:广东省2022年普通高中学业水平模拟试卷数学试题一
广东省2022年普通高中学业水平模拟试卷数学试题一山东省潍坊市寿光现代中学2018-2019学年高一下学期开学考试数学试题(已下线)专题41 空间点、直线、平面的位置关系(同步练习)-2021年高考一轮数学(理)单元复习一遍过(已下线)专题40 空间点、直线、平面的位置关系(知识梳理)-2021年高考一轮数学(理)单元复习一遍过(已下线)专题41 空间点、直线、平面的位置关系(同步练习)-2021年高考一轮数学单元复习一遍过(新高考地区专用)(已下线)专题41 空间点、直线、平面的位置关系(同步练习)-2021年高考一轮数学(文)单元复习一遍过(已下线)第12练 空间直线、平面的垂直-2022年【暑假分层作业】高一数学(人教A版2019必修第二册)
3 . 如图,三棱锥
中,
,
,
,
,
是
的中点,点
在线段
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/b2d58a2a-4ae4-4288-a1b7-b45ff2bdce35.png?resizew=183)
(1)求证:
;
(2)若
平面
, 求四棱锥
的体积.
(参考公式:锥体的体积公式
,其中
是底面积,
是高.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83640592853a53872d7af69c0cffc1bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a916d31a199e250556fb7478d9f57f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71c3c9fe52ad7ab87da571a72c4eea2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60b4c1ae9c57d51e27bbdb001122d3bd.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/b2d58a2a-4ae4-4288-a1b7-b45ff2bdce35.png?resizew=183)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccbd1316b9d1f0c1e71fd078deec61f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba3ff72c2a9cc6f2a593083bed79f78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01293cde79a1d2f59f8d78c893b9523d.png)
(参考公式:锥体的体积公式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f7309683ff41a94e5c5cfeabaeda52a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
您最近一年使用:0次
2019-04-10更新
|
1311次组卷
|
3卷引用:【省级联考】广东省2019届高三一月普通高中学业水平考试数学试题
18-19高一·全国·单元测试
名校
4 . 如图,四边形ABCD为矩形,DA⊥平面ABE,AE=EB=BC=2,BF⊥平面ACE于点F,且点F在CE上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/c1669e1a-ea7e-41e5-940a-2d55e6238bd4.png?resizew=170)
(1)求证:AE⊥BE;
(2)求三棱锥D-AEC的体积.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/c1669e1a-ea7e-41e5-940a-2d55e6238bd4.png?resizew=170)
(1)求证:AE⊥BE;
(2)求三棱锥D-AEC的体积.
您最近一年使用:0次
2019-02-08更新
|
525次组卷
|
4卷引用:2023年广东省普通高中学业水平合格性考试模拟(五)数学试题
2023年广东省普通高中学业水平合格性考试模拟(五)数学试题(已下线)章末检测2(课后作业)-2018-2019版数学创新设计课堂讲义同步系列(人教A版必修2)四川省自贡市田家柄中学教育集团2021-2022学年高二上学期期中考试数学试题甘肃省民勤县第一中学2023-2024学年高二下学期开学考试数学试题
名校
解题方法
5 . 如图,四棱锥
中,底面ABCD为菱形,
平面ABCD,BD交AC于点E,F是线段PC中点,G为线段EC中点.
Ⅰ
求证:
平面PBD;
Ⅱ
求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bba77c22664cbf2111ee2879bf944f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e4d5332664bede4c408d3226c691ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a69bd75be59ed11e9d1feb582079d56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03e1d5a62f9a6b3e03dfe15a180a316f.png)
![](https://img.xkw.com/dksih/QBM/2019/4/10/2179305606447104/2179577889521664/STEM/8b0a62e7b79047719b3ea3f442f1b689.png?resizew=163)
您最近一年使用:0次
2018-07-02更新
|
1134次组卷
|
8卷引用:2023年广东省普通高中学业水平合格性考试模拟(三)数学试题
6 . 如图,在四棱锥
中,底面
是正方形,
平面
,且
,点
为线段
的中点.
(1)求证:
平面
;
(2)求证:
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/2018/11/27/2084522361585664/2089014872555520/STEM/7efcb83d96084868b4f7476647f83482.png?resizew=177)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30067b7b236d17af8a462f96a58d11bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)求证:
![](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
2018-04-09更新
|
1409次组卷
|
6卷引用:2023年1月广东省普通高中学业水平考试模拟一数学试题
7 . 如图所示,在三棱锥
中,
,
,
为
的中点,
垂直平分
,且
分别交
于点
.
![](https://img.xkw.com/dksih/QBM/2018/1/14/1860165904097280/1862216328994816/STEM/ccbf6737-8688-4bb0-83df-9375d0b3a75d.png?resizew=245)
(1)证明:
;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a6f37213648158634b24b8e39a19fd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c94ff4614059e5e91ed304b150d886.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/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f5889fcf29e5d3a134ba9cee5e925f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://img.xkw.com/dksih/QBM/2018/1/14/1860165904097280/1862216328994816/STEM/ccbf6737-8688-4bb0-83df-9375d0b3a75d.png?resizew=245)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b63ce83647c1fe2fc7b32194d1b4114.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70734a8e672376bb0bd1522e229f86a2.png)
您最近一年使用:0次
2018-01-17更新
|
1096次组卷
|
3卷引用:2018年1月广东省普通高中学业水平考试数学试卷
8 . 如图,已知
平面
,
,
,
且
是
的中点,
.
![](https://img.xkw.com/dksih/QBM/2017/12/7/1833520643481600/1839563489927168/STEM/7f0fe37cfcd54a3bb32e2bd53201e386.png?resizew=228)
(1)求证:
平面
;
(2)求证:平面
平面
;
(3)求此多面体的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0137c721b8d4ea6dca8b7d9761134726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d56fc73da0ba166964ef8f37be9a001.png)
且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f414cce1427646590a7f7144efe2e26.png)
![](https://img.xkw.com/dksih/QBM/2017/12/7/1833520643481600/1839563489927168/STEM/7f0fe37cfcd54a3bb32e2bd53201e386.png?resizew=228)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcafa398cc6b6079883e7ad153eb62d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39282bdf319f30d7bc261e2e3ab3b1e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(3)求此多面体的体积.
您最近一年使用:0次
2017-12-16更新
|
720次组卷
|
7卷引用:广东省广州市2017-2018学年高二上学期学业水平测模拟B数学试题
广东省广州市2017-2018学年高二上学期学业水平测模拟B数学试题(已下线)2014届广东省东莞市高三第二次模拟考试文科数学试卷(已下线)2012届福建省四地六校高三期中联考文科数学试卷(已下线)2015届江西省红色六校高三第一次联考文科数学试卷2015届甘肃省天水市一中高三5月中旬仿真考试文科数学试卷河北省保定市2018届高三下学期第二次模拟数学(文)试题山西省运城市景胜中学2020-2021学年高二上学期9月适应性测试数学试题
9 . 在四棱锥
中,底面
为平行四边形,
,
,
,
.
(Ⅰ)证明:
平面
;
(Ⅱ)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f60f51f795e6688651f5fac8e5b385.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed5640a8df01d0c937c4c0c964906e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832ad9f9ccef5b9f18f44f61209b7a4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/652269dc9c3f48536c17c11b3293fbc1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/56d54b0b-75fc-401d-91dd-734b18699d32.png?resizew=158)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d923a338dd2d2e29336b42574d38448.png)
(Ⅱ)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
您最近一年使用:0次
2017-04-14更新
|
1151次组卷
|
4卷引用:2020年1月广东省普通高中学业水平考试数学模拟卷一
10 . 如图,在三棱锥V-ABC中,平面VAB
平面ABC,
为等边三角形,
,且AC=BC=
,O,M分别为AB,VA的中点.
![](https://img.xkw.com/dksih/QBM/2016/11/11/1573141053112320/1573141058715648/STEM/17a95fd684d543218f0fec5d33d9fc1f.png?resizew=174)
(1)求证:VB//平面MOC;
(2)求三棱锥V-ABC的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f63075fdeeb9e765dd696c4ff43ba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/2016/11/11/1573141053112320/1573141058715648/STEM/17a95fd684d543218f0fec5d33d9fc1f.png?resizew=174)
(1)求证:VB//平面MOC;
(2)求三棱锥V-ABC的体积.
您最近一年使用:0次
2016-12-05更新
|
792次组卷
|
8卷引用:2024年广东省普通高中学业水平合格性考试模拟一数学试题