解题方法
1 . 如图,已知三棱柱
,平面
平面
,
,
,
,
、
分别是
、
的中点.
![](https://img.xkw.com/dksih/QBM/2023/4/23/3222630134636544/3222747541839872/STEM/0c095d1949db478d9916e5d064c139e0.png?resizew=186)
(1)证明:
;
(2)若
求
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/af260e0d98c95d1e092dc4c6d348e3ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4020513c097ba34df4b42e297f892cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70aadc0083a7d87fe96b6b6675ff37c2.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/2023/4/23/3222630134636544/3222747541839872/STEM/0c095d1949db478d9916e5d064c139e0.png?resizew=186)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc90fee532e50d319081d571410421.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec27f90f9ce81784f7b09981c3938b81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3205e4c6328a708c2f7f9bd40bf3762f.png)
您最近一年使用:0次
2023-04-23更新
|
821次组卷
|
2卷引用:四川省乐山市市中区海棠实验中学2023届高三上学期第一次月考数学(文科)模拟试题
2 . 如图,边长为2的正方形ABCD所在的平面与半圆弧CD所在平面垂直,M是CD上异于C,D的点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/3d9fca02-8214-448f-b6ac-df4eab901d81.png?resizew=185)
(1)证明:平面AMD⊥平面BMC;
(2)当三棱锥
体积最大时,求面MAB与面MCD所成二面角的正切值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/3d9fca02-8214-448f-b6ac-df4eab901d81.png?resizew=185)
(1)证明:平面AMD⊥平面BMC;
(2)当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d90f940f5693b22ddf2e7c761887d8.png)
您最近一年使用:0次
2023-03-25更新
|
586次组卷
|
4卷引用:四川省绵阳市南山中学2022-2023学年高二下学期期中考试数学(理)试题
四川省绵阳市南山中学2022-2023学年高二下学期期中考试数学(理)试题贵州省凯里市第一中学2022-2023学年高二下学期第一次月考数学试题湖南省岳阳市平江县颐华高级中学2023-2024学年高三上学期入学考试数学试题(已下线)第6章 空间向量与立体几何 单元测试(B卷重难过关)-【学霸满分】2022-2023学年高二数学下学期重难点专题提优训练(苏教版2019选择性必修第二册)
名校
3 . 如图,在三棱锥
中,平面
平面
,
,
为
的中点,
是边长为
的等边三角形,且
.
;
(2)在棱
上是否存在点
,使二面角
的大小为
?若存在,并求出
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.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/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4807ca16360c0cca436e59d4be98f626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0482d12694d419694ecab90485ab70f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21be01a95cdd3149512bf95d6084fdd6.png)
(2)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/324d453870b345da0c41977290192f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9211e017bd40c8931703f4cbb9c69ef9.png)
您最近一年使用:0次
2023-03-23更新
|
801次组卷
|
5卷引用:四川省泸州市天立学校2023-2024学年高二上学期10月月考数学试题
名校
解题方法
4 . 如图,在斜三棱柱
中,
,侧面
为菱形,且
,点D为棱
的中点,
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/4/57566031-289e-42b7-9c97-9eded641cbc3.png?resizew=183)
(1)若
,
,求三棱锥
的体积;
(2)设平面
与平面ABC的交线为l,求证:l⊥平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40975f7553d8cfa57951b568bae9c464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900e00a3609e6043af1034761d4d65f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/399de2503b8e9b3d6978e231cc1c5ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f96e23f7b5d3b1dcac47c19fd6da8860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/4/57566031-289e-42b7-9c97-9eded641cbc3.png?resizew=183)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41fd676c41d2d644928f014b0fea4689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d79e7020414add95907e061df505ef0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1adf768489b3650ae0bd6cc16fb4baf.png)
(2)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62fd0b510920be6bc60d170c3ff3da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
您最近一年使用:0次
2023-03-02更新
|
1126次组卷
|
5卷引用:四川省泸州市2023届高三下学期第二次教学质量诊断性考试数学(文科)试题
名校
解题方法
5 . 如图,在四棱锥中,底面
为矩形,平面
平面
,
,
,
,
为
中点.
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(2)在棱
![](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/52ab924e3692515bd8be4c36472a959a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47548785e478bc5b9591341a881e3127.png)
您最近一年使用:0次
2023-07-21更新
|
1327次组卷
|
7卷引用:四川省成都市成都市石室中学2021-2022学年高一下学期期末数学试题
四川省成都市成都市石室中学2021-2022学年高一下学期期末数学试题云南省下关第一中学2023-2024学年高二上学期见面考试数学试题(已下线)模块三 专题1 利用空间向量求解探究性问题和最值问题(已下线)第02讲 空间向量的应用(1)(已下线)1.4.1 用空间向量研究直线、平面的位置关系【第三课】(已下线)专题05 用空间向量研究直线、平面的平行、垂直问题10种常见考法归类 - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)(已下线)通关练02 用空间向量的解决平行垂直问题10考点精练(50题) - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)
名校
6 . 已知四棱锥
(如图),四边形ABCD为正方形,面
面ABCD,
,M为AD中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/28/70a6dead-4a0c-44ff-849a-d76293a687eb.png?resizew=202)
(1)求证:
;
(2)求直线PC与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fcc62f1c0536d8f82409e8c8df7beb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/28/70a6dead-4a0c-44ff-849a-d76293a687eb.png?resizew=202)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/789c9c79846abc6ba99cf3e575cdae6f.png)
(2)求直线PC与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03203dd5ac79dd8c6707e4340773359.png)
您最近一年使用:0次
2023-02-26更新
|
771次组卷
|
6卷引用:四川省绵阳市南山中学实验学校2023-2024学年高二上学期期末模拟数学试题(七)
四川省绵阳市南山中学实验学校2023-2024学年高二上学期期末模拟数学试题(七)重庆市主城区七校2022-2023学年高二上学期期末数学试题云南省临沧市民族中学-2022-2023学年高二下学期期中数学试题陕西省西安市周至县第六中学2023-2024学年高二上学期10月月考数学试题云南省大理白族自治州大理市民族中学2023-2024学年高二上学期期中数学试题(已下线)通关练04 空间向量与立体几何大题9考点精练(41题)- 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)
解题方法
7 . 如图,在五面体
中,平面
平面
,四边形
为直角梯形,其中
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/28/e84cebe7-8423-4c64-9e24-bc159ff36b1e.png?resizew=191)
(1)求证:
;
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec43f7352b3a8c194b4c37485fb4ffd8.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/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c800b6aabdc453e2c7e343061e9c6a78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddc91db43eea9ba6f29cb5719e26fa34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574cbcf8ccf5418d1871fb74bb61ee14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d9f10d4ebbc23dacfde5ac5854eed5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/28/e84cebe7-8423-4c64-9e24-bc159ff36b1e.png?resizew=191)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117878cbd8c00f2aabcdf62b487e2dc7.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0b72906641ed13716cfbce50923282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bedde879f99aed69d745d5ec8fe62084.png)
您最近一年使用:0次
名校
8 . 如图1,已知
是直角梯形,
,
,
,D在线段
上,
.将
沿
折起,使平面
平面
,连接PB,PC,设PB的中点为
,如图2所示.对于图2,下列选项错误 的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/25/ba9d52df-b8a7-4a9c-b1dd-5c7a5353258e.png?resizew=345)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a351136b18bc7d3bd5122332772ab23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6956513649811bd1a2f8c3e4ca8793c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6050d456b72249b5c55f729f3e54dc72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf6c62979a7aa534a191d8387a741e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/25/ba9d52df-b8a7-4a9c-b1dd-5c7a5353258e.png?resizew=345)
A.![]() ![]() |
B.![]() ![]() ![]() |
C.![]() |
D.平面![]() ![]() |
您最近一年使用:0次
2023-02-22更新
|
500次组卷
|
2卷引用:四川省南充市2022-2023学年高二上学期期末数学试题
名校
解题方法
9 . 在矩形ABCD中,
,
,点E在CD上,现将
沿AE折起,使面
面ABC,当E从D运动到C,求点D在面ABC上的射影K的轨迹长度为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c771a4feb150ad9cff8d70431c97eb17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec43f7352b3a8c194b4c37485fb4ffd8.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-02-07更新
|
1165次组卷
|
7卷引用:四川省绵阳中学2023届高三上学期1月模拟检测文科数学试题
四川省绵阳中学2023届高三上学期1月模拟检测文科数学试题(已下线)模块五 空间向量与立体几何-3江苏省连云港市赣榆智贤中学2022-2023学年高二下学期3月学情检测数学试题(已下线)专题突破卷21 立体几何的轨迹问题(已下线)重难点突破04 立体几何中的轨迹问题(六大题型)(已下线)专题02 空间动点轨迹8种题型归类-【巅峰课堂】2023-2024学年高二数学上学期期中期末复习讲练测(人教A版2019选择性必修第一册)(已下线)第三章 空间轨迹问题 专题五 微点1 翻折、旋转问题中的轨迹问题【培优版】
名校
解题方法
10 . 如图,在平面四边形
中,
,
,
,现将
沿
折起,并连接
,使得平面
平面
,若三棱锥
的体积为
,则三棱锥
外接球的体积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/9/e44cbf65-c674-427d-bc8d-376d0564912f.png?resizew=277)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e0f53f76f26b7e9a81326c34d0d1d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17580410bf63dba4fe164265afaac4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42ec13ca7115ccd73a9d793758f1c170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/9/e44cbf65-c674-427d-bc8d-376d0564912f.png?resizew=277)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-02-03更新
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3卷引用:四川省成都市第七中学2022-2023学年高三上学期1月月考数学理科试题