名校
解题方法
1 . 如图,在棱长为2的正方体
中,
是棱
的中点,
是
与
的交点.
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e22ebcc4aa98d46366df48f751a5f368.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2978e60a50f25e124aa7e325102b3617.png)
您最近一年使用:0次
7日内更新
|
1245次组卷
|
4卷引用:陕西省西安市第一中学2024届高三第十六次模拟考试数学(文科)试题
陕西省西安市第一中学2024届高三第十六次模拟考试数学(文科)试题陕西省榆林市2022-2023学年高二下学期质量检测文科数学试卷(已下线)核心考点6 立体几何中组合体 A基础卷 (高一期末考试必考的10大核心考点) (已下线)专题08 立体几何异面直线所成角、线面角、面面角及平行和垂直的证明 -《期末真题分类汇编》(北师大版(2019))
解题方法
2 . 如图,在四棱锥
中,底面ABCD是平行四边形,
平面ABCD,
,
,且M,N分别为PD,AC的中点.
平面PBC;
(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/ae00fd202e6c855dea7229d259d216d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac787d2e2e7a898ffe8ed79c0bdc2dd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7826e3c6a53025324df827b39c9f7db7.png)
您最近一年使用:0次
解题方法
3 . 如图,在四棱锥
中,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/adcb658e-3739-475d-ab40-db553701daba.png?resizew=144)
(1)求证:
;
(2)若四棱锥
的体积为12,求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3ed4f6bc8c7f08e80b194b867b0092d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f72c935697ef9ceb633a15b90b19ebc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eee296a7d9fba487f1485c61580196f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/adcb658e-3739-475d-ab40-db553701daba.png?resizew=144)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44f4120c94cb7176dc31fcac387b32e.png)
(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2024-01-25更新
|
392次组卷
|
2卷引用:陕西省汉中市汉台区2024届高三下学期教学质量检测考试数学(理)试题
解题方法
4 . 如图,在四棱锥
中.侧面
⊥底面
,
为等边三角形,四边形
为正方形,且
.
为
的中点,证明:
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a0b29cc24e75be59cbaa5c60a4b4c6e.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
您最近一年使用:0次
解题方法
5 . 已知三棱柱
,如图所示,
是
,上一动点,点
、
分别是
、
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/19/6d5e9480-aff8-44aa-a58d-95fb6415b7e5.png?resizew=133)
(1)求证:
平面
;
(2)当
平面
,且
时,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f3be3dcde7b744f420a588cb8dd5b01.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/19/6d5e9480-aff8-44aa-a58d-95fb6415b7e5.png?resizew=133)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377ca47ae9b5ea2a870b6c0b12cfa010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1638808e8d1e70cb014e09fcfc3ff529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01b3e6218ec86973286a21c409d52a6.png)
您最近一年使用:0次
6 . 如图,多面体
中,四边形
为菱形,
,
,
,
.
平面
;
(2)当
时,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bbaccd578a43b2397c8bdd50592fa07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860cd26630a3172fa079ead357dac4d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68fbbd17c89f03dbb61cd6ffdb9a0344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daee8baa62b5b8d5db41eab0d360ee51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42ce82a4c37365f2d4dea2c4ad2e3288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f84f169e50dc59d4f7a8e1e36f5c847.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1ff7bf8ffc8a04186e3e13c1a6d5ced.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630cbaf628064c66436caa267201bc55.png)
您最近一年使用:0次
2024-03-08更新
|
1875次组卷
|
5卷引用:陕西省西安市第一中学2024届高三第十次模拟考试数学(文)试题
陕西省西安市第一中学2024届高三第十次模拟考试数学(文)试题四川省大数据学考联盟2024届高三第一次质量检测数学(文科)试题四川省绵阳市三台中学校2024届高三下学期第二学月测试文科数学试题(已下线)专题07 空间直线﹑平面的垂直(二)-《知识解读·题型专练》(人教A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)
7 . 已知数列
是公差
不为零的等差数列,其前
项和为
,若
成等比数列,且
.
(1)求数列
的通项公式;
(2)记
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29b1b845916a4b6a18cdfbcd308d09c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52ff4f2d9a76730a7ff5baf43da46f1.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ba3491b99cfbbfa5df0433fe8480d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e672c3d231081d12e44a4211e5ac60bf.png)
您最近一年使用:0次
2024-01-27更新
|
1231次组卷
|
5卷引用:陕西省安康市高新中学2024届高三模拟考试最后一卷理科数学试题
解题方法
8 . 如图,在四棱锥
中,
平面
,底面
是正方形,点E在棱PD上,
,
.
是
的中点;
(2)求直线
与平面
所成角的正弦值.
![](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/137eebd1621a51cc5af32b373d983d2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5113ac6e656002f2d110f08ed753e9e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
您最近一年使用:0次
9 . 在三棱锥
中,
为
的中点.
⊥平面
.
(2)若
,平面
平面
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6766e405512f68c11cdd58cb12bc964d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa16146cb21f11693feffb0876c0795b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762cd2d2e0550938fe77347b4a3a42ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
您最近一年使用:0次
2024-01-21更新
|
1454次组卷
|
9卷引用:陕西省榆林市2024届高三一模数学(文)试题
陕西省榆林市2024届高三一模数学(文)试题陕西省汉中市2024届高三上学期第四次校际联考数学(文)试题(已下线)第18讲 第八章 立体几何初步 章节验收测评卷-【帮课堂】(人教A版2019必修第二册)(已下线)13.3 空间图形的表面积和体积(2)-【帮课堂】(苏教版2019必修第二册)(已下线)专题07 空间直线﹑平面的垂直(二)-《知识解读·题型专练》(人教A版2019必修第二册)(已下线)第13章 立体几何初步(基础卷)-重难点突破及混淆易错规避(苏教版2019必修第二册)(已下线)6.5.2平面与平面垂直-【帮课堂】(北师大版2019必修第二册)(已下线)第13章 立体几何初步 章末题型归纳总结 (1)-【帮课堂】(苏教版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)
10 . 如图,在长方体
中,
,
和
交于点E,F为AB的中点.
(1)求证:
平面
;
(2)已知
与平面
所成角为
,求点A到平面CEF的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480f4df0a32a910db7d39695ffd86665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/22/9f34e889-2a53-43d3-bb05-44fef1b03c95.png?resizew=176)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
您最近一年使用:0次
2023-09-22更新
|
605次组卷
|
5卷引用:陕西省宝鸡市千阳县中学2023届高三第十三次模考数学(文)试题
陕西省宝鸡市千阳县中学2023届高三第十三次模考数学(文)试题福建省福州第二中学2023-2024学年高二上学期第一次月考数学试题福建省福州延安中学2023-2024学年高二上学期期中质量检测数学试题(已下线)第七章 综合测试B(提升卷)(已下线)模块三 专题4 大题分类练(立体几何)基础夯实练