1 . 如图,在四棱锥
中,底面
是正方形,
点
分别为线段
的中点.
![](https://img.xkw.com/dksih/QBM/2021/1/30/2647479761453056/2650331994071040/STEM/189bbade99b64707b5e90f195ade5b6c.png?resizew=170)
(1)求证:
平面
;
(2)求证:平面
平面
;
(3)求三棱锥
的体积
![](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/66b92cf03c9a4fbb2e007be04b98aa12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1457d2e76a5b86de1abf121c51eb9d35.png)
![](https://img.xkw.com/dksih/QBM/2021/1/30/2647479761453056/2650331994071040/STEM/189bbade99b64707b5e90f195ade5b6c.png?resizew=170)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4d781525777c7b5284dffc70b2a28a.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6501f1c913a4ef64957a2f01ab5baa15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2c0089d8eb23cb703c5278aff214cd2.png)
您最近一年使用:0次
2021-02-03更新
|
615次组卷
|
3卷引用:河南省焦作市2020-2021学年高二上学期期末数学文试题
河南省焦作市2020-2021学年高二上学期期末数学文试题陕西省西安市雁塔区第二中学2023-2024学年高二上学期第一阶段测评数学试题(已下线)大题专项训练13:立体几何(证明平行、垂直)-2021届高三数学二轮复习
解题方法
2 . 如图,在四棱锥
中,底面
为直角梯形,
,
,
平面
,
,设点M为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/93a9146d-8dea-49b8-99d7-c8d2124b3ecc.jpg?resizew=189)
(1)若四棱锥
的体积为2,求异面直线
,
所成角的余弦值;
(2)若二面角
的余弦值为
,求
的长.
![](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/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87d11dd7422f4703763abc23d83c7584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/93a9146d-8dea-49b8-99d7-c8d2124b3ecc.jpg?resizew=189)
(1)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c123937cd5c0769090771598d6aee7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08e91d2fa9519a5f48d488176700499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
您最近一年使用:0次
2021-01-28更新
|
94次组卷
|
2卷引用:河南省三门峡市2020-2021学年高二上学期期末数学(理科)试题
3 . 如图,在四棱锥PABCD中,PD⊥底面ABCD,AB∥CD,AB=2,CD=3,M为PC上一点,且PM=2MC.
![](https://img.xkw.com/dksih/QBM/2021/10/11/2827211932180480/2827935238881280/STEM/eda8120aa489443ba7f795d40c738f86.png?resizew=160)
(1)求证:BM∥平面PAD;
(2)若AD=2,PD=3,∠BAD=60°,求三棱锥PADM的体积.
![](https://img.xkw.com/dksih/QBM/2021/10/11/2827211932180480/2827935238881280/STEM/eda8120aa489443ba7f795d40c738f86.png?resizew=160)
(1)求证:BM∥平面PAD;
(2)若AD=2,PD=3,∠BAD=60°,求三棱锥PADM的体积.
您最近一年使用:0次
2021-10-12更新
|
3408次组卷
|
16卷引用:河南省八所名校2021-2022学年高二下学期第四次联考文科数学试题
河南省八所名校2021-2022学年高二下学期第四次联考文科数学试题河南省豫西顶级名校2021-2022学年高二下学期4月联考文科数学试题【全国百强校】河南省安阳市第一中学2018-2019学年高一上学期第二阶段考试数学试题云南省玉溪第一中学2020-2021学年高二上学期期中考试数学(文)试题云南省玉溪第一中学2020-2021学年高二上学期期中考试数学(理)试题江西省上高二中2020-2021学年高二下学期第五次月考数学(文)试题江西省六校2021-2022学年高二上学期期末联考数学(文)试题广东省深圳市南方科技大学附属中学2022-2023学年高二下学期期中数学试题辽宁省沈阳市2018届高三教学质量监测(一)数学文试题人教A版(2019) 必修第二册 过关斩将 第八章 立体几何初步 本章复习提升人教B版(2019) 必修第四册 过关斩将 第十一章 立体几何初步 本章复习提升2019届甘肃省天水市第一中学高三下学期最后一模考前练数学(文)试题(已下线)全册综合测试模拟一-【新教材精创】2019-2020高一数学新教材知识讲学(人教A版必修第二册)-《高中新教材知识讲学》北师大版 必修2 过关斩将 第一章 立体几何初步 本章复习提升四川省眉山市彭山区第一中学2021-2022学年高三上学期10月月考文科数学试题(已下线)模块四 专题5 暑期结束综合检测5(能力卷)
解题方法
4 . 如图,三棱柱
中,侧面
是边长为2的菱形,
平面
,且
,点
为
的中点,
为
与
的交点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/a90a269a-c463-4131-8e8f-b7b492330b15.png?resizew=149)
(1)证明:
平面
;
(2)若
,求三棱锥
的体积.
![](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/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7d857811cbd619f868d951aa7a0ab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/a90a269a-c463-4131-8e8f-b7b492330b15.png?resizew=149)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50eda31bbc3d40f0b305d4ac673fc21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211ad5a06b505b8365a62c1946f3cb7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a9f99fb3252a4b3b7a62e8a675ddce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/682f59fc4d85044aae6082314438eb62.png)
您最近一年使用:0次
2020-12-13更新
|
146次组卷
|
2卷引用:河南省名校联盟2020-2021学年高二上学期期中考试 数学(理科)试题
5 . 甲、乙两人进行比赛,现有两组图形,第一组为一个正方形及其外接圆和内切圆,第二组为一个正方体及其外接球和内切球,甲在第一组图形内部任取一点,则此点在正方形与其外接圆之间得3分,此点在内切圆与正方形之间得2分,此点在内切圆内部得1分,乙在第二组图形内部任取一点,则此点在正方体与其外接球之间得3分,此点在内切球与正方体之间得2分,此点在内切球内部得1分.
(1)分别求出甲得3分的概率和乙得3分的概率;
(2)预估在这种规则下,甲、乙两人谁的得分多.
(1)分别求出甲得3分的概率和乙得3分的概率;
(2)预估在这种规则下,甲、乙两人谁的得分多.
您最近一年使用:0次
名校
解题方法
6 . 如图,在四棱锥
中,底面
是平行四边形,
,侧面
底面
,
,
.
![](https://img.xkw.com/dksih/QBM/2020/8/23/2534261204631552/2542443310964736/STEM/06305e9c-8810-4ede-9ec2-5ba57a5f9a33.png?resizew=153)
(1)求证:
平面
;
(2)过
的平面交
于点
,若
,求三棱锥
的体积.
![](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/c5b0382c28547d3834ca71f3f0677695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e99998f33ad6edab18180627d4903dcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcaa14690732aac2d2b8e2561ebbc047.png)
![](https://img.xkw.com/dksih/QBM/2020/8/23/2534261204631552/2542443310964736/STEM/06305e9c-8810-4ede-9ec2-5ba57a5f9a33.png?resizew=153)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd9f5de9503f4d71588c16b0ac33742a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bffd3b6cf2e17d221c8aaeb70e81ef48.png)
您最近一年使用:0次
2020-09-04更新
|
385次组卷
|
3卷引用:河南省鹤壁市高级中学2020-2021学年高二上学期阶段性检测(二)数学试题
名校
解题方法
7 . 如图,在四棱锥
中,
平面
,四边形
是矩形,
,
,
是
的中点,
,垂足为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/14851c84-bb74-414d-876a-4c80ec992c87.png?resizew=152)
(1)证明:
平面
.
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f392902d611863c6908a48e696e7bd8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/14851c84-bb74-414d-876a-4c80ec992c87.png?resizew=152)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826bf6fa3706921b77ad0eb4fcc206bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68744081315689b14c9c7a2b74100f46.png)
您最近一年使用:0次
2020-08-03更新
|
877次组卷
|
3卷引用:河南省新乡市新乡县第一中学2019-2020学年高二下学期期末考试数学(文)试题
解题方法
8 . 如图,在三棱柱ABC﹣A1B1C1中,侧面ABB1A1和侧面BCC1B1都是边长为2的菱形,且∠BAA1=∠CBB1=
.
![](https://img.xkw.com/dksih/QBM/2020/7/27/2515114414956544/2515491264831488/STEM/b3abc76668254084b7c519b3b90ae0d6.png?resizew=272)
(1)证明:BB1⊥A1C;
(2)若A1C=
.求三棱柱ABC﹣A1B1C1的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://img.xkw.com/dksih/QBM/2020/7/27/2515114414956544/2515491264831488/STEM/b3abc76668254084b7c519b3b90ae0d6.png?resizew=272)
(1)证明:BB1⊥A1C;
(2)若A1C=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
您最近一年使用:0次
2020-07-28更新
|
319次组卷
|
2卷引用:河南省平顶山市2019-2020学年高二(下)期末数学(文科)试题
名校
解题方法
9 . 如图,在三棱柱
中,侧面
底面
,
,且点O为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/23516e39-6b8b-4c3a-9bf9-69cb97703489.png?resizew=223)
(1)证明:
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966570e5df2706ade643c09a3018350b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/23516e39-6b8b-4c3a-9bf9-69cb97703489.png?resizew=223)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5021c7ed2dcd938d00723032b1d71e.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/861d61d2b7b16e12fd97f870fb3fa522.png)
您最近一年使用:0次
2020-07-15更新
|
1274次组卷
|
4卷引用:河南省豫西名校2021-2022学年高二下学期3月联考文科数学试题
解题方法
10 . 如图,在三棱锥
中,底面
是边长为2的等边三角形,
,
,点
,
,
分别为
,
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/c317205e-648a-4948-bfdf-5d8918f521ce.png?resizew=132)
(Ⅰ)求证:
平面
;
(Ⅱ)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3931333820859378ea6723ff3075189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630d82ae0ed6deb825514e0bc92e74a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/c317205e-648a-4948-bfdf-5d8918f521ce.png?resizew=132)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93cf663ee2bf1ac5c43f4306fa0cf250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f957abf297b059c1cc6bfc78416714.png)
(Ⅱ)求三棱锥
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2020-07-14更新
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3卷引用:河南省焦作市2019-2020学年高二下学期学业质量测试(期末) 数学(文)试题