名校
解题方法
1 . 如图,在三棱锥
中,
平面
,
,
.求证:
;
(2)若
,
分别在棱
,
上,且
,
,问在棱
上是否存在一点
,使得
平面
.若存在,则求出
的值;若不存在.请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c71dbf267939080668be464f1aa60da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0530f462e5ec1e58c46e1f7644d0cc21.png)
(2)若
![](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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98de02d1d5b7ac04bce54be393218922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760e8882e84ecd68bc889a55efce5d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d3f076d3f5a78fc081c252e9a55d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/261fbbc173664b0047448fef17763dfb.png)
您最近一年使用:0次
2021-08-07更新
|
607次组卷
|
5卷引用:湖北省荆州市沙市中学2022-2023学年高二上学期第一次月考数学试题
湖北省荆州市沙市中学2022-2023学年高二上学期第一次月考数学试题湖北省荆州市沙市区2022-2023学年高二上学期9月第一次月考数学试题山西省太原市2020-2021学年高一下学期期末数学试题(已下线)一轮复习大题专练46—立体几何(探索性问题2)-2022届高三数学一轮复习贵州省“三新”联盟校2021-2022学年高一下学期期末联考数学试题
2 . 如图,在三棱锥P﹣ABC中,PA⊥AB,PA=1,PC=3,BC=2,sin∠PCA
,E,F,G分别为线段的PC,PB,AB中点,且BE
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/492dc959-0255-417a-be03-e4e589afdb5a.png?resizew=153)
(1)求证:AB⊥BC;
(2)若M为线段BC上一点,求三棱锥M﹣EFG的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34efd0021d06e31448496f3673eb2a45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb6da35cb03b489e795ee5f6b612a11.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/492dc959-0255-417a-be03-e4e589afdb5a.png?resizew=153)
(1)求证:AB⊥BC;
(2)若M为线段BC上一点,求三棱锥M﹣EFG的体积.
您最近一年使用:0次
名校
3 . 如图,在三棱锥A-BCD中,AB=a,AC=AD=b,BC=CD=DB=c(a>0,b>0,c>0)该三棱锥的截面EFGH平行于AB、CD,分别交AD、AC、BC、BD于E、F、G、H.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/458e183f-606d-4fe7-9278-405c2b885d48.png?resizew=159)
(1)证明:AB⊥CD;
(2)求截面四边形EFGH面积的最大值,并说明面积取最大值时截面的位置.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/458e183f-606d-4fe7-9278-405c2b885d48.png?resizew=159)
(1)证明:AB⊥CD;
(2)求截面四边形EFGH面积的最大值,并说明面积取最大值时截面的位置.
您最近一年使用:0次
名校
4 . 如图,三棱柱
中,侧面
为菱形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/4c9c8269-3f64-4aa0-bae4-64ce6fb6a3b5.png?resizew=202)
(1)证明:
;
(2)若
,
,
,求二面角
的余弦值的绝对值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7870cee007535b979d35bc7feab75616.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/4c9c8269-3f64-4aa0-bae4-64ce6fb6a3b5.png?resizew=202)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ee347187fbbfe9e8a6faf286795d79.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7fd49bb962841b4575805030e19add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2e238b2757353026133bbe495645e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69418f38ada198be25a69cb651e33e04.png)
您最近一年使用:0次
2019-07-12更新
|
709次组卷
|
10卷引用:【全国百强校】湖北省荆州中学2018-2019学年高二上学期期末考试数学(理)试题
【全国百强校】湖北省荆州中学2018-2019学年高二上学期期末考试数学(理)试题2015-2016学年河南省许昌高中等校高二下第一次联考理科数学试卷四川省成都市第七中学2017届高三三诊模拟数学(理)试题四川省遂宁市2017-2018学年高二上学期期末考试数学理试题河北省武邑中学2017-2018学年高二上学期期末考试数学(理)试题河南师范大学附属中学2017-2018学年高二4月月考数学(理)试题四川省遂宁市2017-2018学年高二上学期教学水平监测数学(理)试题【全国百强校】广东省湛江第一中学2018-2019学年高二上学期第二次大考数学(理)试题(B卷)四川省成都市第七中学2019年高三零诊模拟数学(理)试题河北省沧州市肃宁一中2019-2020学年高二上学期第四次月考数学试题
5 . 如图所示,已知四边形
是直角梯形,
,
,其中
是
上的一点,四边形
是菱形,满足
,沿
将
折起,使
.
![](https://img.xkw.com/dksih/QBM/2018/10/8/2049187022299136/2052178546024448/STEM/1c54b1c0eb6c4a3bb9fb71834abf1a5e.png?resizew=212)
(1)求证:平面
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37591109b0a0ec5ffe2133f83310eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/210306c006ece33f301e297ed7d24434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0650097b0f8f5b2e6e27003adce30929.png)
![](https://img.xkw.com/dksih/QBM/2018/10/8/2049187022299136/2052178546024448/STEM/1c54b1c0eb6c4a3bb9fb71834abf1a5e.png?resizew=212)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b348d4333ecdfc3e3b1ba16dc312550d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ff27eea7545bb06f9472f91290c54e.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86b3c6811325e29d79b2d89c42bcee0.png)
您最近一年使用:0次
名校
6 . 如果有一天我们分居异面直线的两头,那我一定穿越时空的阻隔,画条公垂线向你冲来,一刻也不愿逗留.如图1所示,在梯形
中,
//
,且
,
,分别延长两腰交于点
,点
为线段
上的一点,将
沿
折起到
的位置,使
,如图2所示.
![](https://img.xkw.com/dksih/QBM/2018/6/2/1958637280600064/2001040938942464/STEM/e6db4d788d40467b976c0fdef6d06da1.png?resizew=148)
![](https://img.xkw.com/dksih/QBM/2018/6/2/1958637280600064/2001040938942464/STEM/2437b18a7b544db1a59be6175f351b5a.png?resizew=175)
(1)求证:
;
(2)若
,
,四棱锥
的体积为
,求四棱锥
的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/950e82a0f9712457f2dd9f8a93f8a217.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa2a83fed9bf4cb09d84a980452e346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3f7be7700b3b4177237b841636ccc5d.png)
![](https://img.xkw.com/dksih/QBM/2018/6/2/1958637280600064/2001040938942464/STEM/e6db4d788d40467b976c0fdef6d06da1.png?resizew=148)
![](https://img.xkw.com/dksih/QBM/2018/6/2/1958637280600064/2001040938942464/STEM/2437b18a7b544db1a59be6175f351b5a.png?resizew=175)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/206b3689e55f0ad11910f7a5519671af.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4494a85de0be0b97a69348115aef8513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db2b1c641b93caae9b7a82441e4ba70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e7dc603317eb90974c75efec9f02b1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db2b1c641b93caae9b7a82441e4ba70.png)
您最近一年使用:0次
名校
7 . 如图所示,在三棱柱
中,侧面
与侧面
都是菱形,
,
.
(Ⅰ)求证:
;
(Ⅱ)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede6a60cad0e0b58e1549fda6e085719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce731cd45eb83b75e47e20551a97cd45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8c5b66af3944a4b655055967f958c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb3d814a5e87bf9969c779c306a27a81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3ced5c98bec7ba2cb7ea0c9bf7389e.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af58726507c48cbb7cfad266680e4d17.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7909074a79d1834f4993489578574112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b13e8f385766fb73e9db98b65a8f732.png)
您最近一年使用:0次
2016-12-03更新
|
1588次组卷
|
8卷引用:湖北省荆州市沙市中学2017-2018学年高二上学期期中数学(文)试题