名校
解题方法
1 . 如图,在四面体A-BCD中,AB⊥平面BCD,BC⊥CD,BC=2,∠CBD=
,E、F、Q分别为BC、BD、AB边的中点,P为AD边上任意一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/d4af287d-9e2d-4522-a3b7-9bfd785b4b2a.png?resizew=148)
(1)证明:CP
平面QEF.
(2)当二面角B-QF-E的平面角为
时,求AB的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/d4af287d-9e2d-4522-a3b7-9bfd785b4b2a.png?resizew=148)
(1)证明:CP
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
(2)当二面角B-QF-E的平面角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
您最近一年使用:0次
2021-12-04更新
|
1323次组卷
|
6卷引用:重庆市南开中学校2021-2022学年高一下学期7月月考数学试题
名校
2 . 五棱锥
中,
,
,
,
,
,
,
,平面
平面
,
为
的中点,
(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/a1eedae784fbb992bb62dace87e4d459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e6932fbc0ea31c28a51c302b287c936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e1a6cd95707c57e85eafd43f7b9fbcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7459cac5a01a137bff696095281e57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e70eb7baf5d3973fcaf5fc152156508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0725fa4642ac0223c4095f90e65523e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f020ca4ad44801691235958e253907d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb34d6d26481113c0ac4af0366f72e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/11/a4f88ec2-c8cd-4616-a561-f96f1412301e.png?resizew=186)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0285afe567ca0b32f0ccafc30167cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/149596fee6ed1e2d19fd8dadc14a8baf.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/149596fee6ed1e2d19fd8dadc14a8baf.png)
您最近一年使用:0次
解题方法
3 . 如图,在四棱锥
中,侧面
底面ABCD,侧面PAB是边长为1的等边三角形,底面ABCD是正方形,
是侧棱PB上的点,
是底面对角线AC上的点,且
,
.
(1)求证:
;
(2)求证:
平面PAD;
(3)求点
到平面PAD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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4eebde0291ae62d02a498b56358ece.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ac7b134d8d1136f90233addaa4723f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/28/4a9ebc2f-c120-4160-a426-37f01d69be62.png?resizew=193)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfa54114f04a75b8c96165b3718ed7f.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
解题方法
4 . 如图所示,正方形ADEF与梯形ABCD所在的平面互相垂直,已知
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/73e79a0f-8581-4fa1-a9e6-d307229998c3.png?resizew=215)
(1)求证:
平面
;
(2)连接
,求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffda707068a4a1778e79da6f20fb86d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/73e79a0f-8581-4fa1-a9e6-d307229998c3.png?resizew=215)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8ccd4181f956f6e0140bf0ab8f0716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
您最近一年使用:0次
2022-05-07更新
|
596次组卷
|
3卷引用:重庆市缙云教育联盟2021-2022学年高一下学期5月质量检测数学试题
名校
5 . 在矩形
中,
点
分别在
上,且
.沿
将四边形
翻折至四边形
,点
平面
.
![](https://img.xkw.com/dksih/QBM/2021/7/8/2759900325306368/2777778682167296/STEM/055aee96639749ab9bfe87ca48f553d5.png?resizew=482)
(1)求证:
平面
;
(2)
四点是否共面?给出结论,并给予证明;
(3)在翻折的过程中,设二面角
的平面角为
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554f455de1180a8a6245b24ec9480a7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cf34605ceb15a969300a1121fc74f22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/946c16d99496d31ce4d87301a4793393.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c76e6c67644b8bad9bfe11c7ec3081d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7829855159327b2a87c3a424b3f7134a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28d6477c85c5a4ac410a884e92fbe53.png)
![](https://img.xkw.com/dksih/QBM/2021/7/8/2759900325306368/2777778682167296/STEM/055aee96639749ab9bfe87ca48f553d5.png?resizew=482)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f235281692aa274a672d57fc400bd45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b12cffc313a181f666e3fc8e66b6f59.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45a8c036e6d2c152d0a16dbbe2bff905.png)
(3)在翻折的过程中,设二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b43ff5a9a70210b4017c4c38b4258c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc24d605ad707ad0e76059d8a31f50d3.png)
您最近一年使用:0次
2021-08-02更新
|
541次组卷
|
2卷引用:重庆市第八中学校2021-2022学年高一下学期第二次月考数学试题
名校
解题方法
6 . 如图1,在矩形
中,已知
,
,点
,
分别在边
,
上,且
,将梯形
沿
折起,使
在平面
上的射影
恰好落在线段
靠近
的三等分点处,得到图2中的立体图形.
(1)
(2)![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/6d0764c0-11e6-45cf-a30b-d86d3f5db126.png?resizew=138)
(1)在图2中,求证:
平面
;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e6cdf1dd2efb03e3663452c46a4532f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bedde879f99aed69d745d5ec8fe62084.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/6aaa0e41-f9c2-4d79-9421-fe2a2b977dfd.png?resizew=187)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/6d0764c0-11e6-45cf-a30b-d86d3f5db126.png?resizew=138)
(1)在图2中,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/321302db9ce1bf9ef167c0d3831d5154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/370148e9147aa25c60a07ab4ad46e83d.png)
您最近一年使用:0次
名校
7 . 如图,四棱锥P-ABCD中,底面ABCD为矩形,PD⊥平面ABCD,点E、F分别是AB和PC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/961c6f82-b6fa-4f7c-939c-4cb71f36f319.png?resizew=191)
(1)求证:AB⊥平面PAD;
(2)求证:EF//平面PAD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/961c6f82-b6fa-4f7c-939c-4cb71f36f319.png?resizew=191)
(1)求证:AB⊥平面PAD;
(2)求证:EF//平面PAD.
您最近一年使用:0次
2019-10-04更新
|
908次组卷
|
6卷引用:重庆市渝北区松树桥中学校2019-2020学年高二上学期第一次段考考数学试题
8 . 如图,三棱柱
中侧棱与底面垂直,且
,AB⊥AC,M,N,P分别为
,BC,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/f3af5590-c08d-40c4-92e7-a33fcfaa25fd.png?resizew=149)
(1)求证:PN∥面
;
(2)求平面PMN与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9d2462e6dbd321cf3abae25a56adf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc916a3eb3cabc632e7c894320d5e412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/f3af5590-c08d-40c4-92e7-a33fcfaa25fd.png?resizew=149)
(1)求证:PN∥面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(2)求平面PMN与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
您最近一年使用:0次
名校
9 . 圆柱
中,
为圆
的直径,
、
、
都是圆柱
的母线,
.
![](https://img.xkw.com/dksih/QBM/2022/2/3/2908238868004864/2940484600758272/STEM/27f7ecddedec402ab3ac837ad964fc1c.png?resizew=206)
(1)求证
平面
;
(2)若
,求锐二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1642eec556eb252de9c1ab7bb5ca90b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735056c174e8dd7906257a2a50a962a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4083c581c6027c4b2ae7e3b3749f485.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b46b2ff7904a600687703d536dd603.png)
![](https://img.xkw.com/dksih/QBM/2022/2/3/2908238868004864/2940484600758272/STEM/27f7ecddedec402ab3ac837ad964fc1c.png?resizew=206)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15d8662513d307ed16683319e997494d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd943c914d3a080719c8fcda4b2cb3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8e82d52f3b44b7cd6b9f2cc1788e2e.png)
您最近一年使用:0次
名校
10 . 如图,多面体ABCDEF中,DE⊥平面ABCD,底面ABCD是菱形,AB=2,∠BAD=60°,四边形BDEF是正方形.
![](https://img.xkw.com/dksih/QBM/2021/11/19/2854712830689280/2857331093274624/STEM/7aa19aee-ce29-46f3-b057-822b4ac118c0.png?resizew=258)
(1)求证;CF∥平面AED;
(2)求直线AF与平面ECF所成角的正弦值.
![](https://img.xkw.com/dksih/QBM/2021/11/19/2854712830689280/2857331093274624/STEM/7aa19aee-ce29-46f3-b057-822b4ac118c0.png?resizew=258)
(1)求证;CF∥平面AED;
(2)求直线AF与平面ECF所成角的正弦值.
您最近一年使用:0次
2021-11-23更新
|
314次组卷
|
4卷引用:重庆市朝阳中学2021-2022学年高二上学期10月月考数学试题