1 . 已知
为等腰直角三角形,
,
,
分别为
和
上的点,且
,
,如图1.沿EF将
折起使平面
平面
,连接
,
,如图2.
![](https://img.xkw.com/dksih/QBM/2021/9/7/2802926553350144/2803656190033920/STEM/6ab3d0d549a04c9bb12d765487232be3.png?resizew=387)
(1)求异面直线
与
所成角的余弦值;
(2)已知
为棱
上一点,试确定
的位置,使
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08313da7b66283d2e0b3987f3e6761f4.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1364213f546b37f8764ddcb59e36ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13bd9e8b54864ca44115d24a5aeeb83c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6501f1c913a4ef64957a2f01ab5baa15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b312dab930cbbb9a4bb1a99f044dab73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2021/9/7/2802926553350144/2803656190033920/STEM/6ab3d0d549a04c9bb12d765487232be3.png?resizew=387)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0285afe567ca0b32f0ccafc30167cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20af148464904e21f4374cc8fb886fba.png)
您最近一年使用:0次
2021-09-08更新
|
729次组卷
|
2卷引用:江苏省百校联考2021-2022学年高三上学期第一次考试数学试题
解题方法
2 . 如图,多面体
是由三棱柱
截去部分后而成,D是
的中点.
(1)若
平面
,求点C到平面
的距离;
(2)如图,点E在线段
上,且
,点F在
上,且
,问
为何值时,
∥平面
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e3ff5b7a53ef89d72fbc2cef3cbdbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/11/aecf3969-a8c1-45d6-80d3-927621b48bc9.png?resizew=159)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba1a99ed62d0daa3dee3c2833d2e1c3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/535a3700e6d20d0beefaae8f57dea2e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dddfef906818cc8ddd00f867b77f227.png)
(2)如图,点E在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3696f3ae3de7529611929d0b4e7b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf825bea2da10773df06c70624e64c3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dddfef906818cc8ddd00f867b77f227.png)
您最近一年使用:0次
3 . 如图,四棱锥
中,底面
是边长为2的正方形,平面
平面
,
.
![](https://img.xkw.com/dksih/QBM/2022/3/15/2936669072900096/2938915202899968/STEM/f92f38925624423e8463721d6aa039d7.png?resizew=260)
(1)若M,N分别为
的中点,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
平面
;
(2)求二面角
的正弦值.
![](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/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1328e05d150f86dbe18656662eaa8f6b.png)
![](https://img.xkw.com/dksih/QBM/2022/3/15/2936669072900096/2938915202899968/STEM/f92f38925624423e8463721d6aa039d7.png?resizew=260)
(1)若M,N分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47891397990336f55f96bd66d367758b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1069d514c3c32aeabd274475ee209ed6.png)
您最近一年使用:0次
2022-03-18更新
|
454次组卷
|
2卷引用:辽宁省凌源市2022届高三下学期开学抽测考试数学试题
名校
4 . 如图,多面体
中,四边形
为平行四边形,
,
,四边形
为梯形,
,
,
,
,
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/24/5ad85ab5-0687-4a02-b424-7c57e08cf6ca.png?resizew=240)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](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/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/921a71040d18df8b33bc41995675a586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d5a164bf56f8fb92527ad78bc10ccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dced11455b3e31a9090915f80a046fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6370d6c626bdabf1fc694501ee6c714f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56512504254ab7f574a717dd6830fb33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2f82cd6b3572de264a1fbf7f39f0afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/24/5ad85ab5-0687-4a02-b424-7c57e08cf6ca.png?resizew=240)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c34b18525831f3eda7bb90be0199b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
您最近一年使用:0次
5 . 如图,在四棱锥
中,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/2/1bdb9ab3-806f-46dc-924c-05ee2176642a.png?resizew=196)
(1)若
为
中点,
为
中点,
,求证:
平面
;
(2)若平面
平面
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f9045e6cd575bbe76c89ef6ef852fd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7bd02e0adeae92ba9526261b1baf797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032b3e422eeb39cf649dffc9934a7cf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5590d0226850c341940e6d9cbab180bf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/2/1bdb9ab3-806f-46dc-924c-05ee2176642a.png?resizew=196)
(1)若
![](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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c97a7fab5d1550e2fef66772cc985fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2cb00dc421f44e30228aa26a532582c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31effd1d3f7ce1f6e57be80c7f3af4ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/324d453870b345da0c41977290192f94.png)
您最近一年使用:0次
名校
解题方法
6 . 如图,四棱锥
的底面是矩形,平面
平面
,E,F分别是
的中点.
![](https://img.xkw.com/dksih/QBM/2022/1/21/2899377870831616/2909306660012032/STEM/9b3edcb6-eb57-4209-9e6c-f40b98d2a52e.png?resizew=195)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
:
(2)求点P到平面
的距离.
![](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/e98b0b77d5910a7afe5da22c4586095d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7366da07065712da11602f4afce8cbed.png)
![](https://img.xkw.com/dksih/QBM/2022/1/21/2899377870831616/2909306660012032/STEM/9b3edcb6-eb57-4209-9e6c-f40b98d2a52e.png?resizew=195)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求点P到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
您最近一年使用:0次
2022-02-04更新
|
429次组卷
|
2卷引用:安徽省滁州市定远县育才学校2021-2022学年高三下学期开学考试数学(文)试题
名校
解题方法
7 . 如图,边长为
的等边
所在平面与菱形
所在平面互相垂直,且
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/10/915d88ac-80df-46d6-ae7f-523fec1081d4.png?resizew=216)
(1)求证:
平面
;
(2)求多面体
的体积
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1433137fef4e88aa38f2503cec900358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7579755d7d17bd72d97b03df323aefa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e302e173e60f3e6136369d0c4908d5ac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/10/915d88ac-80df-46d6-ae7f-523fec1081d4.png?resizew=216)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3521d6f223a2d7f597f8613c4530dd1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
您最近一年使用:0次
2020-08-27更新
|
797次组卷
|
14卷引用:四川省泸州市泸县第四中学2024届高三下学期开学考试数学(文)试题
四川省泸州市泸县第四中学2024届高三下学期开学考试数学(文)试题安徽省合肥市2020届高三高考数学(文科)三模试题(已下线)专题20+立体几何综合-2020年高考数学(文)母题题源解密(全国Ⅱ专版)安徽省合肥市2020届高三下学期第三次教学质量检测数学(文)试题陕西省宝鸡市渭滨区2021届高三下学期适应性训练(一)文科数学试题黑龙江省实验中学2021届高三下学期四模数学(文)试题陕西省西安中学2021届高三下学期第八次模拟考试文科数学试题四川省仁寿第一中学校南校区2020-2021学年高二5月第二次质量检测数学(文)试题陕西省安康中学2021-2022学年高二上学期第一次月考数学试题(已下线)专题8-5 立体几何大题15种归类(平行、垂直、体积、动点、最值等非建系)-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)湖南省长沙市宁乡市三校(宁乡七中、九中、十中)2021-2022学年高一下学期期中数学试题河南省中原名校联盟2021-2022学年高三下学期4月适应性联考文科数学试题(已下线)专题20 立体几何综合-2020年高考数学(文)母题题源解密(全国Ⅱ专版)宁夏银川市第二中学2023届高三模拟数学(文)试题
名校
解题方法
8 . 如图,梯形ABCD中,
,
,
,
,DE⊥AB,垂足为点E.将△AED沿DE折起,使得点A到点P的位置,且PE⊥EB,连接PB,PC,M,
分别为PC和EB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/30/8140688b-1d9b-43cf-8c3f-0f6732a0b858.png?resizew=374)
(1)证明:
平面PED;
(2)求点C到平面DNM的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9723a6e093c297b001436e8932b1820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ad8d16722f5b9e7fd2602f14d5ffbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e530783dc49238736ed5c1157e6184dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/30/8140688b-1d9b-43cf-8c3f-0f6732a0b858.png?resizew=374)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eaa5e336f830a3e5cd60ff7a756f3ef.png)
(2)求点C到平面DNM的距离.
您最近一年使用:0次
2022-08-29更新
|
381次组卷
|
4卷引用:河南省百校联盟2023届高三上学期开学摸底联考全国卷文科数学试题
解题方法
9 . 如图,在三棱柱
中,
,D为
中点,四边形
为正方形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/30/b3b86a94-a34a-40e1-9b61-a2f824c39653.png?resizew=145)
(1)求证:
平面
;
(2)再从条件①、条件②这两个条件中选择一个作为已知,求直线
与平面
所成角的正弦值.
条件①:
;
条件②:
.
注:如果选择条件①和条件②分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19313eda8aed25d59b3a1c59a3117634.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/30/b3b86a94-a34a-40e1-9b61-a2f824c39653.png?resizew=145)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/547a4b438e2e6687c7cd55ea08bbaae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)再从条件①、条件②这两个条件中选择一个作为已知,求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7870cee007535b979d35bc7feab75616.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eabd2314dbe8bf1ef6e37a7befbb0c61.png)
注:如果选择条件①和条件②分别解答,按第一个解答计分.
您最近一年使用:0次
名校
10 . 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:福建省厦门第六中学2021-2022学年高二上学期开学适应性练习数学试题