名校
解题方法
1 . 如图,在三棱锥D-ABC中,已知△BCD是正三角形,AB⊥平面BCD,AB=BC=a,E为BC的中点,F在棱AC上,且AF=3FC.
(2)求三棱锥A-BDF的体积;
(3)若M为DB的中点,是否存在N在棱AC上,
,且
平面DEF?若存在,求
的值并说明理由;若不存在,给出证明.
(2)求三棱锥A-BDF的体积;
(3)若M为DB的中点,是否存在N在棱AC上,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18da88f27cc36dbf1d01bcea7341bc37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db9cf9de9a49a343865199c29b329797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
解题方法
2 . 如图,在四棱锥
中,底面
为菱形,
,
,
,
平面
,点M,N,H分别在棱PB,PD,PC上,且
.
;
(2)连接AC交BD于点O,连接OP.求证:
平面
;
(3)若H为PC的中点,PA与平面
所成角为60°,四棱锥
被平面
截为两部分,记四棱锥
体积为
,另一部分体积为
,求
.
![](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/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb96e0331eebe80ed1ff610faf531fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debdc6632a4877e5131d3da25cda8b89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edd68fe22ed9909165aedc98d1d8e3a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828247a3338571cb0d4ba2a5bf88929c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec6297cf195e60fd53375a501deb2ac.png)
(2)连接AC交BD于点O,连接OP.求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc6f007dbf1c1a36eb031e520608403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)若H为PC的中点,PA与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edd68fe22ed9909165aedc98d1d8e3a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73bb075576cc0f585bda44277ac1d098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737b04ce09bc7e1ed86dc9b3c85203b.png)
您最近一年使用:0次
名校
3 . 如图,
为矩形,
为梯形,平面
平面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/16/e203ce5f-037d-48c8-bb07-1f35f66669d4.png?resizew=202)
(1)若M为
中点,求证:
平面
;
(2)设平面
平面
,试判断
与平面
能否垂直?并证明你的结论;
(3)在(1)条件下,求平面
与平面
所夹的锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5bf51c07144386bd23a422d9ceb140.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6379891c7150af4188b5ab746d703bae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d20fec32122b4a70b993976201c9ba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0046177466c78f08d45449dc5639bf38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe7a201432af0a2f9d21c6803906f5c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/16/e203ce5f-037d-48c8-bb07-1f35f66669d4.png?resizew=202)
(1)若M为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8197bf06d017950c85c3ba6a291c095e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df21b7b7a47318ef2bb069450c39f1cd.png)
(2)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c659d2ab07b9b66ed9a60cb604dd9aa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b951997af111a840cb333a082137402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)在(1)条件下,求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df21b7b7a47318ef2bb069450c39f1cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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名校
解题方法
4 . 如图,在四棱锥
中,
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/10/77f0ef14-6bcd-4653-9638-91b27200afd9.png?resizew=226)
(1)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
平面
,证明:点
为棱
的中点;
(2)已知二面角
的大小为
,当平面
和平面
的夹角为
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0998d16d7bf13acae5bfb9b8de55ca04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4d5ff57f147aa0628fdd47899b5a132.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/10/77f0ef14-6bcd-4653-9638-91b27200afd9.png?resizew=226)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(2)已知二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f479b251fdb01bae6d16abb7f2d694a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6943f158bf2f76abed0c58196dbe0bc5.png)
您最近一年使用:0次
2023-04-10更新
|
471次组卷
|
3卷引用:江西省吉安市2023届高三模拟测试数学(理)(一模)试题
名校
解题方法
5 . 如图,在直三棱柱
中,
,
.
![](https://img.xkw.com/dksih/QBM/2022/9/12/3064881370423296/3066134020325376/STEM/aae63029e9094b7bbe50b06144b84441.png?resizew=240)
(1)设平面
与平面ABC的交线为l,判断l与AC的位置关系,并证明;
(2)求证:
;
(3)若
与平面
所成的角为30°,求三棱锥
内切球的表面积S.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1240a927e5540d2dce76ba019f6cf82.png)
![](https://img.xkw.com/dksih/QBM/2022/9/12/3064881370423296/3066134020325376/STEM/aae63029e9094b7bbe50b06144b84441.png?resizew=240)
(1)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e862713d078c4f06ec1f15ccd6f5a1f7.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38593653bedb845ecfa820806a29a1e.png)
您最近一年使用:0次
2022-09-14更新
|
1900次组卷
|
6卷引用:山东省临沂市2021-2022学年高一下学期期末数学试题
山东省临沂市2021-2022学年高一下学期期末数学试题(已下线)必修二全册综合测试卷(提高篇)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)(已下线)模块五 专题2 全真能力模拟(人教B)(已下线)期末专题09 立体几何大题综合-【备战期末必刷真题】(已下线)宁夏回族自治区石嘴山市第三中学2022-2023学年高一下学期期末考试数学试卷宁夏石嘴山市第三中学2022-2023学年高一下学期期末数学试题
名校
解题方法
6 . 几何体
是四棱锥,
为正三角形,
,
,
为线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/c4f92b87-66db-461f-886d-891d1f5c9957.png?resizew=144)
(1)求证:
平面
;
(2)线段
上是否存在一点
,使得
四点共面?若存在,请找出点
,并证明;若不存在,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ad8d16722f5b9e7fd2602f14d5ffbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b0382c28547d3834ca71f3f0677695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/c4f92b87-66db-461f-886d-891d1f5c9957.png?resizew=144)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba8f7af0e091e082100c3cd7f8c487f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a814b70236a108be5d6e7ff271fe92.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9635120b0064caffba6d42091833d069.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
2022-11-03更新
|
975次组卷
|
4卷引用:四川省峨眉第二中学校2022-2023学年高二上学期10月月考理科数学试题
四川省峨眉第二中学校2022-2023学年高二上学期10月月考理科数学试题黑龙江省哈尔滨市宾县第二中学2022-2023学年高三上学期期中考试数学试题(已下线)8.5.3平面与平面平行(精练)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)(已下线)第26讲 空间直线、平面的平行的判定4种常见方法
名校
解题方法
7 . 如图,在四棱锥
中,底面
是正方形,过
的平面与侧棱
的交点分别是
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/6fae32b1-d807-431b-8449-457a3eef0a4b.png?resizew=163)
(1)证明:
;
(2)若
底面
,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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc72cba412508818056817a70552176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/6fae32b1-d807-431b-8449-457a3eef0a4b.png?resizew=163)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee73452ee4d5437f1399f1235b95e55f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
您最近一年使用:0次
2022-11-02更新
|
690次组卷
|
3卷引用:北京市房山区2022-2023学年高二上学期学业水平调研(期中)考试数学试题
8 . (1)请用文字语言叙述平面与平面平行的判定定理;
(2)把(1)中的定理写成“已知:⋯⋯ ,求证: ⋯⋯ ”的形式, 并用反证法证明.
(2)把(1)中的定理写成“已知:⋯⋯ ,求证: ⋯⋯ ”的形式, 并用反证法证明.
您最近一年使用:0次
2023-01-02更新
|
268次组卷
|
4卷引用:上海市奉贤中学2021-2022学年高二上学期期中数学试题
上海市奉贤中学2021-2022学年高二上学期期中数学试题上海市嘉定区第一中学2021-2022学年高二上学期期中数学试题上海市嘉定区第一中学2023-2024学年高二上学期期中数学试题(已下线)第10章 空间直线与平面(单元重点综合测试)-2023-2024学年高二数学单元速记·巧练(沪教版2020必修第三册)
名校
解题方法
9 . 如图所示,在四棱锥P
ABCD中,底面ABCD是∠DAB=60°且边长为
的菱形,侧面PAD为正三角形,其所在的平面垂直于底面ABCD.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/8e840a11-4094-44e7-a891-60a94a13ce96.png?resizew=188)
(1)若G为AD边的中点,求证:BG⊥平面PAD;
(2)若E为BC边的中点,能否在棱PC上找一点F,使得PA//平面DEF?并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b700fa9aeb1016aa71f76e4b6bb212e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/8e840a11-4094-44e7-a891-60a94a13ce96.png?resizew=188)
(1)若G为AD边的中点,求证:BG⊥平面PAD;
(2)若E为BC边的中点,能否在棱PC上找一点F,使得PA//平面DEF?并证明你的结论.
您最近一年使用:0次
2022-11-02更新
|
796次组卷
|
6卷引用:四川省眉山市仁寿第一中学南校区2022-2023学年高二上学期期中考试数学(理)试题
四川省眉山市仁寿第一中学南校区2022-2023学年高二上学期期中考试数学(理)试题四川省眉山市仁寿第一中学南校区2022-2023学年高二上学期期中考试数学(文)试题(已下线)专题8-4 非建系型:探索性平行与垂直证明及求角度(已下线)8.6.3平面与平面垂直(第2课时平面与平面垂直的性质定理)(精练)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)(已下线)专题09 基本图形的平行与垂直-期中期末考点大串讲(苏教版2019必修第二册)江西省丰城中学2022-2023学年高一下学期期末考试数学试题
名校
解题方法
10 . 如图所示,已知四边形ABCD是正方形,四边形ACEF是矩形,M是线段EF的中点.
平面BDE;
(2)若平面
平面
,平面
平面
,试分析l与m的位置关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac480d8d9d7821b62a603cf5cfda236.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac3e2deda1ce6ec95b5e89220e826b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48abba67b697688749cf92b8c7205161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24462999a96dfae3b4123ef4c59a48ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2685e63e66cd2c9a048590bc0f16d.png)
您最近一年使用:0次
2022-05-03更新
|
985次组卷
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6卷引用:福建省漳州第三中学2021-2022学年高一下学期期中考试数学试题
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