解题方法
1 . 如图,棱台
中,
,底面ABCD是边长为4的正方形,底面
是边长为2的正方形,连接
,BD,
.
(1)证明:
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7929b25566f051e25a63ad341470523a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d609847e2ff3d64e5a514582c3ead0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c92b5799d12ea37de46d7c942ce7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/288abe01824f42cfe725509af5aec4cd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/16/ea55b6c1-0ece-4cfc-bcf9-98ab561004e6.png?resizew=158)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/555dfe77eeb168a880694e22bd9acbdd.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9271e2c743a961a5abe3edb752cbe2.png)
您最近一年使用:0次
2023-09-15更新
|
262次组卷
|
2卷引用:贵州省遵义市2023届高三第三次统考文科数学试题
解题方法
2 . 如图甲,在矩形
中,
,
是
的中点,将
沿直线
翻折后得到四棱锥
,如图乙,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/12/6ee5635c-587a-431c-a7e2-a9991b9d1a58.png?resizew=451)
(1)求证:
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d58da37b3d1dbd2fee75089d5ba28134.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/d631f45bc652539853f236952afa5bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efeadd146662b5d8fe14a424138ef751.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08aa6fd52f3933cbded9ce8c880b4a10.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/12/6ee5635c-587a-431c-a7e2-a9991b9d1a58.png?resizew=451)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d5ee2d6fcbcad17b69997ef0741d2d.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba759550d6c10ffd2922b936888f3973.png)
您最近一年使用:0次
解题方法
3 . 矩形ABCD中,
(如图1),将
沿AC折到
的位置,点
在平面ABC上的射影E在AB边上,连结
(如图2).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/11/29f10317-e6c8-4431-83a8-b538640f68f9.png?resizew=406)
(1)证明:
;
(2)过
的平面与BC平行,作出该平面截三棱锥
所得截面(不要求写作法).记截面分三棱锥所得两部分的体积分别为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d598a5d19c4ea839623aed430aa96d8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/644f63756fe9251e65cc14e1ce9723d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3d4de4f2a11ce4dd04c334e2680483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c597ff77c65c5add6f50294e3eee9536.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/11/29f10317-e6c8-4431-83a8-b538640f68f9.png?resizew=406)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d994a45f95ec665cc70801ed8134bcd0.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15dc61d5de97b5a40be925b278ae494c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ebd86a076448d19401268f139b5b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1414761ee01932fc70f428a91955d6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737b04ce09bc7e1ed86dc9b3c85203b.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,在边长为
的正方体
中,
为
中点,
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f11f1840eb8b17e7b07c3fe7e987a9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0625187f35c80fb49277693e6b41b021.png)
您最近一年使用:0次
2024-04-24更新
|
2866次组卷
|
21卷引用:贵州省黔西南州2022-2023学年高一下学期期末教学质量检测数学试题
贵州省黔西南州2022-2023学年高一下学期期末教学质量检测数学试题广西桂林市第十八中学2019-2020学年高一上学期期中数学试题河北省唐山市滦南县第一中学2020-2021学年高一下学期期中数学试题湖南省邵阳市第二中学2021-2022学年高一下学期期中数学试题河北省邯郸市大名县第一中学2021-2022学年高一下学期开学考试数学试题河南省信阳市信阳高级中学2021-2022学年高一下学期第四次月考数学试题新疆昌吉回族自治州昌吉市昌吉州行知学校2022-2023学年高三上学期1月学业水平考试数学试题云南省(新教材)2021-2022学年高一春季学期期末普通高中学业水平考试数学试题浙江省绍兴蕺山外国语学校2022-2023学年高一下学期期中数学试题福建省永春第二中学2022-2023学年高一下学期5月月考数学试题云南省文山州砚山县第三高级中学2022-2023学年高二下学期5月月考数学试题专题07B立体几何解答题(已下线)第03讲 直线、平面平行的判定与性质(八大题型)(讲义)重庆市梁平中学2023-2024学年高二上学期入学考试数学试题(已下线)8.5.2 直线与平面平行-同步题型分类归纳讲与练(人教A版2019必修第二册)(已下线)第13章 立体几何初步(提升卷)-重难点突破及混淆易错规避(苏教版2019必修第二册)(已下线)6.6简单几何体的再认识-【帮课堂】(北师大版2019必修第二册)(已下线)第8.5.2讲 直线与平面平行-同步精讲精练宝典(人教A版2019必修第二册)(已下线)专题06 立体几何初步解答题热点题型-《期末真题分类汇编》(江苏专用)广东省茂名市信宜市第二中学2023-2024学年高一下学期5月月考数学试题云南省玉溪市通海一中、江川一中、易门一中三校2023-2024学年高一下学期六月联考数学试卷
名校
解题方法
5 . 如图,在直三棱柱
中,
,
,
,M,N分别是
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/23/d4920206-3b1f-4eab-b3da-5babedcfc9a7.png?resizew=152)
(1)求证:
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca38004c7744a7567bef30f0674fe60f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3cc9cccfb4c260dac05f4ed57e8c10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/23/d4920206-3b1f-4eab-b3da-5babedcfc9a7.png?resizew=152)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce9ebc509c57beab91d0833dba1b2c6.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9112e61822a648db4979de272f69cbea.png)
您最近一年使用:0次
2022-08-22更新
|
454次组卷
|
4卷引用:贵州省贵阳市2023届高三上学期8月摸底考试数学(文)试题
6 . 如图,四棱锥
的底面
是矩形,
平面
,
.
![](https://img.xkw.com/dksih/QBM/2022/7/15/3023254720167936/3026700605685760/STEM/35c7e430ebe44103b612d46bc45ef548.png?resizew=221)
(1)求证:
;
(2)求三棱锥
的体积;
(3)求平面
和平面
夹角的余弦值的大小.
![](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/d5ef03497414d454933f76684ee16970.png)
![](https://img.xkw.com/dksih/QBM/2022/7/15/3023254720167936/3026700605685760/STEM/35c7e430ebe44103b612d46bc45ef548.png?resizew=221)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/712f7375b4ede5f75c0d81870c0f86af.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b568ba5f8e290c966a4fcd4a46005c7.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
解题方法
7 . 如图,在四棱锥
中,
,
是边长为
的正三角形,平面
平面
,
,点
,
,
分别是线段
,
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/d6b27c4c-0e3e-468f-b0b5-e3b6ab241445.png?resizew=193)
(1)求证:点
在平面
内;
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb99353e3076643c832c8973ac8a6c1.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/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/d6b27c4c-0e3e-468f-b0b5-e3b6ab241445.png?resizew=193)
(1)求证:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e375fa6cd4a05814744169b157686077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8504651146697b0ecca4f789790d41ed.png)
您最近一年使用:0次
8 . 已知三棱锥D-ABC,△ABC与△ABD都是等边三角形,AB=2.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/29/436adf57-234a-4e1b-a7ff-b7bb68f5ccb6.png?resizew=145)
(1)若
,求证:平面ABC⊥平面ABD;
(2)若AD⊥BC,求三棱锥D-ABC的体积.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/29/436adf57-234a-4e1b-a7ff-b7bb68f5ccb6.png?resizew=145)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18834f4ba51bf4d490f35ed02379fec7.png)
(2)若AD⊥BC,求三棱锥D-ABC的体积.
您最近一年使用:0次
2022-03-11更新
|
1217次组卷
|
6卷引用:贵州省贵阳市2022届高三适应性监测考试(一)数学(文)试题
贵州省贵阳市2022届高三适应性监测考试(一)数学(文)试题高考广西桂林、崇左市2022届高三5月联合模拟考试数学(文)试题(已下线)第8.6讲 空间直线、平面的垂直-2021-2022学年高一数学链接教材精准变式练(人教A版2019必修第二册)广东省揭阳市惠来县第一中学2021-2022学年高一下学期第二次阶段考数学试题新疆塔城市第三中学2022-2023学年高二上学期期中数学试题陕西省部分学校2024届高三下学期高考仿真模拟(一)文科数学试题(全国卷)
名校
解题方法
9 . 已知菱形
的边长为
,
,如图1.沿对角线
将
向上折起至
,连接
,构成一个四面体
,如图2.
;
(2)若
,求四面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c967c9b3f669ea78edd838e1d8b59e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db4c18aba9681a8475968248764d4c3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417104247ce266ae42c3a9860f387272.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685534ba47e83433200ce29660875118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db4c18aba9681a8475968248764d4c3a.png)
您最近一年使用:0次
2021-11-13更新
|
1019次组卷
|
7卷引用:贵州省贵州师范大学附属中学2021-2022学年高二10月月考数学(理)试题
名校
解题方法
10 . 如图所示,在三棱柱
中,M为棱
的中点.
![](https://img.xkw.com/dksih/QBM/2021/6/14/2742622851866624/2743036705185792/STEM/f83cddb709ab405f8eb506f80a2379a0.png?resizew=241)
(1)求证∶![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
平面
;
(2)若
⊥平面ABC,
,AB=AC=AA1=2,求点B到平面AB1M的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/2021/6/14/2742622851866624/2743036705185792/STEM/f83cddb709ab405f8eb506f80a2379a0.png?resizew=241)
(1)求证∶
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770b4f16694b2bd79a1a93d776a82680.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
您最近一年使用:0次
2021-06-14更新
|
1243次组卷
|
4卷引用:贵州省黔东南自治州镇远县文德民族中学校2022届高三上学期期末数学(文)试题
贵州省黔东南自治州镇远县文德民族中学校2022届高三上学期期末数学(文)试题安徽省100名校2020届高三下学期攻疫联考数学(文)试题(已下线)考点32 直线、平面平行的判定及其性质-备战2022年高考数学(文)一轮复习考点帮湖北省武汉外国语学校2020-2021学年高一下学期期末数学试题