名校
解题方法
1 . 如图,在四棱锥
中,
平面ABCD,
,
,
,
,E是棱PB上一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/206c7cb9-3649-46b8-8b6d-848d2cc7a335.png?resizew=144)
(1)求证:平面
平面PBC;
(2)若E是PB的中点,求直线PA与平面EAC所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4ab7e657f01bdfa235f8c4d6681d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ce41a735b5b77c5dc72680a6903d36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f144992e1cbee34868abce1e5ad38c9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/206c7cb9-3649-46b8-8b6d-848d2cc7a335.png?resizew=144)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677d1863ff4d8ac1604b18149d4f320f.png)
(2)若E是PB的中点,求直线PA与平面EAC所成角的正弦值.
您最近一年使用:0次
2022-11-27更新
|
567次组卷
|
7卷引用:青海省西宁市大通县2024届高三上学期开学摸底考试数学(理科)试题
名校
解题方法
2 . 如图,在四棱锥
中,底面
为矩形,
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/5f0d7f00-d30a-4173-a266-90dac832ac88.png?resizew=140)
(1)证明:平面
平面
;
(2)若
为
中点,求二面角
的平面角的余弦值.
![](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/6666079cf2c78be72f3f5e5f46e1031c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/5f0d7f00-d30a-4173-a266-90dac832ac88.png?resizew=140)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4d781525777c7b5284dffc70b2a28a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a86cd1f401153b192de90246f4da53.png)
您最近一年使用:0次
2023-02-14更新
|
146次组卷
|
4卷引用:青海省西宁市大通回族土族自治县2022-2023学年高二上学期期末考试数学(理)试题
青海省西宁市大通回族土族自治县2022-2023学年高二上学期期末考试数学(理)试题陕西省榆林市府谷中学2022-2023学年高二上学期第二次月考理科数学试题内蒙古乌兰浩特市第四中学2022-2023学年高二下学期第一次月考数学(理)试题(已下线)陕西省西安市铁一中学2023-2024学年高三上学期第二次月考理科数学试题变式题19-22
3 . 如图,在直三棱柱
中,
是等边三角形,
,
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/9/d07a6973-c647-4649-939d-3f6aea373694.png?resizew=153)
(1)证明:平面
平面
.
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f41d364b55d88688cd1f571ed231228.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/9/d07a6973-c647-4649-939d-3f6aea373694.png?resizew=153)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f3c1b59a81027f370cb0f205892e76e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
您最近一年使用:0次
2022-12-09更新
|
1062次组卷
|
6卷引用:青海省海东市2022-2023学年高三上学期12月第一次模拟数学(文)试题
青海省海东市2022-2023学年高三上学期12月第一次模拟数学(文)试题四川省2023届高三高考专家联测卷(三)文科数学试题(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)(精讲)-【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)广西柳州市鹿寨县鹿鸣中学2022-2023学年高二上学期期末考试模拟(一)卷数学试题(已下线)8.6.3 平面与平面垂直(2)-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(人教A版2019必修第二册)甘肃省定西市临洮县2024届高三下学期开学假期学习质量检测数学试题
名校
解题方法
4 . 如图,在长方体ABCD-A1B1C1D1中,AB=2BC=2CC1=2,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/2022/9/28/3076339012116480/3076375830126592/STEM/9d473c73ff1c4065916be317fc21c5c5.png?resizew=266)
(1)求点D到平面AD1E的距离;
(2)求证:平面AD1E⊥平面EBB1.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://img.xkw.com/dksih/QBM/2022/9/28/3076339012116480/3076375830126592/STEM/9d473c73ff1c4065916be317fc21c5c5.png?resizew=266)
(1)求点D到平面AD1E的距离;
(2)求证:平面AD1E⊥平面EBB1.
您最近一年使用:0次
2022-09-28更新
|
964次组卷
|
6卷引用:青海省西宁市城西区青海湟川中学2022-2023学年高二上学期12月月考数学试题
5 . 如图,正四棱锥
中.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/14/92c340fe-bf62-4e59-9153-22c585c440b7.png?resizew=212)
(1)求证:平面PAC⊥平面PBD;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/14/92c340fe-bf62-4e59-9153-22c585c440b7.png?resizew=212)
(1)求证:平面PAC⊥平面PBD;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9801cabc43c024b9c5fac34b7db5d69b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d7d6e5be7914a224e94a7b7e409a79c.png)
您最近一年使用:0次
2022-07-08更新
|
890次组卷
|
4卷引用:青海省西宁市2022-2023学年高一下学期期末调研测试数学试题
青海省西宁市2022-2023学年高一下学期期末调研测试数学试题重庆市长寿区2021-2022学年高一下学期期末数学(B)试题(已下线)微专题16 利用传统方法轻松搞定二面角问题(已下线)2023年高考全国乙卷数学(理)真题变式题16-20
解题方法
6 . 如图,在四棱锥
中,
,
,
是等边三角形,
,
.
![](https://img.xkw.com/dksih/QBM/2022/5/21/2989841019691008/2998252334342144/STEM/9f3462f9-d248-46f6-afa1-2d9728c590f7.png?resizew=175)
(1)求证:平面
平面ABCD;
(2)求点C到平面PBD的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57d754536ccb873ca18ea9e39bcd3bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfa54114f04a75b8c96165b3718ed7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d8a07e0ed59625cc85c8d310117a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e306e30d3159e4a68435c3fcfc8da693.png)
![](https://img.xkw.com/dksih/QBM/2022/5/21/2989841019691008/2998252334342144/STEM/9f3462f9-d248-46f6-afa1-2d9728c590f7.png?resizew=175)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
(2)求点C到平面PBD的距离.
您最近一年使用:0次
名校
解题方法
7 . 如图,四边形ABCD是正方形,AF⊥平面ABCD,
,AB=AF=2CE,H点为FB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/1/b0943bd9-e4ea-4210-863c-2531a51d017e.png?resizew=192)
(1)证明:平面AEH⊥平面FBC;
(2)试问在线段EF(不含端点)上是否存在一点P,使得
平面FBD.若存在,请指出点P的位置;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5d02468072783e4c6d0ab7c93e83350.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/1/b0943bd9-e4ea-4210-863c-2531a51d017e.png?resizew=192)
(1)证明:平面AEH⊥平面FBC;
(2)试问在线段EF(不含端点)上是否存在一点P,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfe5c83cd2ce829ba559292786a1eeb.png)
您最近一年使用:0次
2022-07-20更新
|
355次组卷
|
5卷引用:青海省海东市第一中学2022-2023学年高二上学期12月期中考试数学试题
名校
8 . 如图,在直四棱柱
中,
平面
,底面
是菱形,且
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/8/a396892f-c0a7-4fe4-ba70-40be0c70de4f.png?resizew=250)
(1)求证:
∥平面
;
(2)求证:平面
平面
;
(3)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/8a8bfe2553e852df73185d017c0a62fb.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/9a69138b166b2a53d994189c8eb29358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/8/a396892f-c0a7-4fe4-ba70-40be0c70de4f.png?resizew=250)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb66e4fa5ca4231b8ce2490eeb192b.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5cdffeb1fdad9935a00d40c9d650655.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb66e4fa5ca4231b8ce2490eeb192b.png)
您最近一年使用:0次
2022-07-07更新
|
1510次组卷
|
5卷引用:青海省西宁市湟中区多巴高级中学2023-2024学年高二上学期第一次月考数学试题
9 . 如图,在三棱柱
中,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/23/ca38b5ad-aef1-44a4-bebb-200dd08eb2ef.png?resizew=259)
(1)证明:平面
平面
.
(2)设P是棱
的中点,求AC与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bceb86f6a01109700263e97177c335eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b29e8a1eefb6776168969a1155c9e9c5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/23/ca38b5ad-aef1-44a4-bebb-200dd08eb2ef.png?resizew=259)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
(2)设P是棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d041feacf189306d130f4a949880bfc8.png)
您最近一年使用:0次
10 . 如图,在三棱柱
中,
,
.
![](https://img.xkw.com/dksih/QBM/2022/6/20/3005515608031232/3007421490274304/STEM/460b1813006a40b892ed197776819035.png?resizew=253)
(1)证明:平面
平面
.
(2)设P是棱
上一点,且
,求三棱锥
体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fd31113c6f65e8b5ce30935f50df64c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b29e8a1eefb6776168969a1155c9e9c5.png)
![](https://img.xkw.com/dksih/QBM/2022/6/20/3005515608031232/3007421490274304/STEM/460b1813006a40b892ed197776819035.png?resizew=253)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
(2)设P是棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b3ed8c86401d4cce99cb51c3a25478c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b31232447a0b0b3e45a0e111c60e7f0.png)
您最近一年使用:0次
2022-06-23更新
|
2595次组卷
|
8卷引用:青海省海东市第一中学2022届高考模拟(一)数学(文)试题
青海省海东市第一中学2022届高考模拟(一)数学(文)试题贵州省黔东南苗族侗族自治州2021-2022学年高一下学期期末考试数学试题(已下线)专题28 空间几何体的结构特征、表面积与体积-3(已下线)7.2 空间几何中的垂直(精练)(已下线)专题31 直线、平面垂直的判定与性质-2(已下线)专题3 空间几何体的体积运算(提升版)(已下线)上海市静安区2023届高三二模数学试题变式题16-21广东省佛山市实验中学2024届高三上学期第五次月考数学试题