名校
1 . 如图,已知
为正三角形,D为AB的中点,E在AC上,且
,现沿DE将
折起,折起过程中点A仍然记作点A,使得平面
平面BCED,在折起后的图形中.
![](https://img.xkw.com/dksih/QBM/2021/9/13/2807128439554048/2815225309601792/STEM/80d94deb-2f09-4c04-872f-88daac4f7a21.png?resizew=472)
(1)在AC上是否存在点M,使得直线
平面ABD.若存在,求出点M的位置;若不存在,说明理由.
(2)求平面ABD与平面ACE所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb8f6c9335373be2e09046a1e51424f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://img.xkw.com/dksih/QBM/2021/9/13/2807128439554048/2815225309601792/STEM/80d94deb-2f09-4c04-872f-88daac4f7a21.png?resizew=472)
(1)在AC上是否存在点M,使得直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6dfed58659a9cab4d1836c3d2effdc.png)
(2)求平面ABD与平面ACE所成锐二面角的余弦值.
您最近一年使用:0次
2021-09-24更新
|
526次组卷
|
2卷引用:安徽省宿州市砀山中学2021-2022学年高二上学期第一次质量检测数学试题
解题方法
2 . 如图,在边长为2的正方体
中,点
为
的中点,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/9afd5e22-14e3-4ee5-a5c3-15ba35ff7f59.png?resizew=180)
(1)证明:
平面
;
(2)若
为侧面
内一点,且
平面
,求
的最小值.
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554b3b4c5ce7aca81becc07ed4903736.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/9afd5e22-14e3-4ee5-a5c3-15ba35ff7f59.png?resizew=180)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808709d61dda984c341792168f67104f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f33fa5152ba27f7b8a28890cefca219.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b7f5d3a32de5e2f05c86d2e9cd94f80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,在四棱锥
中,
,
,
,
平面
,E为PD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/b473418a-2d80-4fb1-bb41-57257e6b4a1f.png?resizew=159)
(Ⅰ)证明:
平面
;
(Ⅱ)若
,求点E到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810227b082bd14dbcde85c3181841571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/b473418a-2d80-4fb1-bb41-57257e6b4a1f.png?resizew=159)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c34b18525831f3eda7bb90be0199b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/672757753ee4387ac9ce54467663a82c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2021-08-12更新
|
1074次组卷
|
7卷引用:安徽省阜阳市太和第一中学2020-2021学年高三上学期二模数学(文)试题
解题方法
4 . 如图,在三棱柱
中,
底面ABC,
,且
,满足
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/b71b5b69-3260-40b5-8ab0-6739d4b9b5a1.png?resizew=158)
(1)证明:
.
(2)若G为侧面
上一动点,且EG
平面
,求点G在侧面
上运动的轨迹长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b9ce838d7f2790addb9fc0107229525.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b9896d55490c61667c58b8545267c8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dea49fe6561fdc4266f7cee518e0d77.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/b71b5b69-3260-40b5-8ab0-6739d4b9b5a1.png?resizew=158)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca08229da992fdd08d6cb1efeb469b1.png)
(2)若G为侧面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab145f9eeadbd74f61a92c1a5f07c4a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
您最近一年使用:0次
2021-02-27更新
|
366次组卷
|
3卷引用:安徽省芜湖市2020-2021学年高二上学期期末理科数学试题
安徽省芜湖市2020-2021学年高二上学期期末理科数学试题安徽省滁州市定远县育才学校2021-2022学年高三下学期第二次月考数学(理)试题(已下线)第三章 空间轨迹问题 专题三 立体几何轨迹长度问题 微点2 立体几何轨迹长度问题综合训练【培优版】
解题方法
5 . 如图,在直四棱柱(侧棱垂直底面的棱柱称为直棱柱)
中,底面是边长为2的菱形,且
,
,点E,F分别为
,
的中点,点G在
上.
![](https://img.xkw.com/dksih/QBM/2021/2/1/2648806308118528/2649944575016960/STEM/084769ef689b4ef3b22b8cd67391d7de.png?resizew=152)
(1)证明:
平面ACE.
(2)求三棱锥B-ACE的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeed487430a5b8a330f2d0c52166521a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/408871c2b71ef88d6f556ce53cf73cc9.png)
![](https://img.xkw.com/dksih/QBM/2021/2/1/2648806308118528/2649944575016960/STEM/084769ef689b4ef3b22b8cd67391d7de.png?resizew=152)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55537f7dbac74c17fe0dc386dcdab3fa.png)
(2)求三棱锥B-ACE的体积.
您最近一年使用:0次
6 . 如图,在直三棱柱
中,点
、
分别为
和
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/dc67479f-01e4-4abd-8307-1cf201bdd9ea.png?resizew=201)
(1)证明:
平面
;
(2)若
,
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/dc67479f-01e4-4abd-8307-1cf201bdd9ea.png?resizew=201)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d355b4c58b4e883b9e65cc6da8622e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e384e0ffc3d599303b77ee2a12221e.png)
您最近一年使用:0次
2020-09-25更新
|
932次组卷
|
3卷引用:安徽省滁州市定远县育才学校2021届高三下学期最后一模理科数学试题
名校
7 . 如图,在正方体
中,点E、F分别为是
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/14/4a9a441d-14a3-4f39-b032-8ec4de72761d.png?resizew=162)
(1)证明:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64265fe16d0d3eadd213f2d6529e07fa.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/14/4a9a441d-14a3-4f39-b032-8ec4de72761d.png?resizew=162)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/349740b9aa8c242258eb07cb7224c3f6.png)
您最近一年使用:0次
名校
8 . 如图,在菱形
中,
,平面
平面
是线段
的中点,
.
![](https://img.xkw.com/dksih/QBM/2020/4/23/2447897895649280/2448171207032832/STEM/c2f7d1afd8c84714ba3c52f8ac110fce.png?resizew=174)
(1)证明:
平面
.
(2)求直线
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbbef63825ad9230972f4bb31a549c74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c1acdd27cebb11e0266464b03b3afb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2293bdd1209e807b3392e4b6e9faa8a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc356feeed0c605c2ddf28d3940bcdc.png)
![](https://img.xkw.com/dksih/QBM/2020/4/23/2447897895649280/2448171207032832/STEM/c2f7d1afd8c84714ba3c52f8ac110fce.png?resizew=174)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0457394ce4f2dc8d940c565c94dcf557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
您最近一年使用:0次
2020-04-24更新
|
283次组卷
|
2卷引用:安徽省淮北市第一中学2019-2020学年高三下学期第五次考试数学(理)试题
名校
解题方法
9 . 如图,已知直四棱柱ABCD﹣A1B1C1D1的底面是直角梯形,AB⊥BC,AB∥CD,E,F分别是棱BC,B1C1上的动点,且EF∥CC1,CD=DD1=1,AB=2,BC=3.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/a55afa23-55a1-492a-866f-09e9e24de02d.png?resizew=234)
(1)证明:无论点E怎样运动,四边形EFD1D都为矩形;
(2)当EC=1时,求几何体A﹣EFD1D的体积.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/a55afa23-55a1-492a-866f-09e9e24de02d.png?resizew=234)
(1)证明:无论点E怎样运动,四边形EFD1D都为矩形;
(2)当EC=1时,求几何体A﹣EFD1D的体积.
您最近一年使用:0次
名校
10 . 如图,在三棱台ABC﹣A1B1C1中,D,E分别是AB,AC的中点,B1E⊥平面ABC,△AB1C是等边三角形,AB=2A1B1,AC=2BC,∠ACB=90°.
![](https://img.xkw.com/dksih/QBM/2019/1/3/2110811852365824/2111689648562176/STEM/91a9089e0c8a45e083aad6aad30ce27c.png?resizew=183)
(1)证明:B1C∥平面A1DE;
(2)求二面角A﹣BB1﹣C的正弦值.
![](https://img.xkw.com/dksih/QBM/2019/1/3/2110811852365824/2111689648562176/STEM/91a9089e0c8a45e083aad6aad30ce27c.png?resizew=183)
(1)证明:B1C∥平面A1DE;
(2)求二面角A﹣BB1﹣C的正弦值.
您最近一年使用:0次
2018-12-03更新
|
1282次组卷
|
6卷引用:安徽省阜阳市太和中学2019-2020学年高二下学期开学考试数学(理)试题