名校
解题方法
1 . 对于数集
,其中
,
,定义向量集
,若对任意
,存在
,使得
,则称
具有性质
.
(1)已知数集
,请写出数集
对应的向量集
,并判断
是否具有性质
(不需要证明).
(2)若
,且
具有性质
,求
的值;
(3)若
具有性质
,且
,
为常数且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f7a53ccddc5210a37f12e3ab6e99df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d3fe482c5e20abfc9f89c876f653ae3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c5751a1b2fb31063f3360f4ef5b0274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c122d308af408739c2717376e932122d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c6bb4424eb1e5ab02b8ac83fd6ad10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8de3dabcc3150fd539ac97718ba10c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(1)已知数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c40ffb95d55e922a408458c19940dbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096b1ece1dcd29c59a46a4b3e02cb548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/351bb3f3c54604330fa5b6c2bc3a7502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096b1ece1dcd29c59a46a4b3e02cb548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17bda892497cea43df67db57b4e2a07a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73eecc365f7e94267552eb430f2034e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6734531288c894a5edb143104e448ce6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b68031c3405c23f82fb3f352e44a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaa18be2cbabe89d886b99241c4dca28.png)
您最近一年使用:0次
2 .
个有次序的实数
,
,
,
所组成的有序数组
,
,
,
称为一个
维向量,其中
,2,
,
称为该向量的第
个分量.特别地,对一个
维向量
,若
,
,
,称
为
维信号向量.设
,
,则
和
的内积定义为
,且
.
(1)直接写出4个两两垂直的4维信号向量.
(2)证明:不存在6个两两垂直的6维信号向量.
(3)已知
个两两垂直的2024维信号向量
,
,
,
满足它们的前
个分量都是相同的,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de5b983949f56bc3137d48e72a393b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11e3810cf1eca832ef7487d354e474d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/811ba47ff724fd153378ffe14c1e0b9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/713ac1eb0d8cce55d51e62ef4a2b1634.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42b3123092bbc1c62e30b0253edd09b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80bd9ca5f1ebecf069be3b25efafd29a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6460555341932b6b590af7d74b8f0db7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42b3123092bbc1c62e30b0253edd09b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3507f3193277c2f2a5e9d83d25cc9366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b73255f197b518efc343bc9776837e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cfce6ff54e403e1486244d51395bed.png)
(1)直接写出4个两两垂直的4维信号向量.
(2)证明:不存在6个两两垂直的6维信号向量.
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596afe6f8149e39c53d36a759bee6151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2182d0dad848ccc76944d976befbf2.png)
您最近一年使用:0次
2024-05-03更新
|
380次组卷
|
3卷引用:重庆市乌江新高考协作体2023-2024学年高一下学期5月期中数学试题
重庆市乌江新高考协作体2023-2024学年高一下学期5月期中数学试题上海市进才中学2023-2024学年高一下学期期中数学试题(已下线)专题03 高一下期末考前必刷卷01(基础卷)-期末考点大串讲(人教A版2019必修第二册)
3 . 小明在学习矩形时发现:在矩形
中,点
是
边上一点,过点
作
交边
于点
,若
,则
平分
.他的证明思路是:利用矩形的性质得三角形全等,再利用边角转化使问题得以解决.请根据小明的思路完成以下作图与填空.
(1)用直尺和圆规,过点
作
的垂线交
于点
;(只保留作图痕迹)
(2)已知:如图,在矩形
中,点
是
边上一点,过点
作
交边
于点
.求证:
平分
;
证明:
四边形
是矩形,
,
①_________________
.
,
,
,
②_________________.
又
,③_________________,
④_________________
.
.
又
,
,
.
⑤_________________,
.
.
平分
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992a19339adac3a2f1aab1fbc11b1c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f805768a5ffaf8bdfa4bc3b680aafdc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3981e7286d41960daf4e110c1c84e03a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/6/9eb8f234-3821-48d3-8637-3cca31a02ef7.png?resizew=155)
(1)用直尺和圆规,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(2)已知:如图,在矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992a19339adac3a2f1aab1fbc11b1c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b48e4874d9f210d8ce6ee784a47e8588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3981e7286d41960daf4e110c1c84e03a.png)
证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f3d198e76391779fa3badc848c8ac8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deeeb5318d4077995233dabb715f854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c515a84858c394146ed2ca984916cdf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83873a9d782f2588c5eedbfe73f9bc2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/587aa905348cc7cd1333e7472a57430a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f95cf1631aee3f6b55b0435e1da9442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00d80f47b98c1b4bc66cc0bc86c2cd2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
又
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df7a0621aafbc7e55cd6f6b9686c214b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a755b788551f0f6d022f1b6ba557dd8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b68af712817ab23370b394227723e61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a54012359305f6200e9811a4e03ab3f.png)
又
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e9dd6147fd83173b71cc7467e481b3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0091d0711859cb2c619b8c3846c44051.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9287a2c4832bc0c48c9768acc6aa5ccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f3d198e76391779fa3badc848c8ac8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14f4108d0dfb537295bbd3f08b407be3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18184310094795a3abb3a09974ab8b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6911a6519903fb7e464ab74e873996a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3981e7286d41960daf4e110c1c84e03a.png)
您最近一年使用:0次
名校
4 . 《见微知著》谈到:从一个简单的经典问题出发,从特殊到一般,由简单到复杂:从部分到整体,由低维到高维,知识与方法上的类比是探索发展的重要途径,是思想阀门发现新问题、新结论的重要方法,
阅读材料一:利用整体思想解题,运用代数式的恒等变形,使不少依照常规思路难以解决的问题找到简便解决方法,常用的途径有:(1)整体观察;(2)整体设元;(3)整体代入:(4)整体求和等.
例如,
,求证:
.
证明:原式
.
波利亚在《怎样解题》中指出:“当你找到第一个藤菇或作出第一个发现后,再四处看看,他们总是成群生长”类似问题,我们有更多的式子满足以上特征.
请根据阅读材料解答下列问题
(1)已知如
,求
___________.
(2)若
,解方程
.
(3)若正数
、
满足
,求
的最小值.
阅读材料一:利用整体思想解题,运用代数式的恒等变形,使不少依照常规思路难以解决的问题找到简便解决方法,常用的途径有:(1)整体观察;(2)整体设元;(3)整体代入:(4)整体求和等.
例如,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca27cc54ca0332245f5167488daa3408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e2764ccd2cfe6de0c53dce98e45b120.png)
证明:原式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87898da3367d13667477a10c9cc47ac2.png)
波利亚在《怎样解题》中指出:“当你找到第一个藤菇或作出第一个发现后,再四处看看,他们总是成群生长”类似问题,我们有更多的式子满足以上特征.
请根据阅读材料解答下列问题
(1)已知如
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca27cc54ca0332245f5167488daa3408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1440907008dbc815bd37e30cb09e8a6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56667aabbe787eb1c3189d487d203e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d9093a255130a938a4d84595c0c56ce.png)
(3)若正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca27cc54ca0332245f5167488daa3408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ab1cbf887eca130c254f6e0cf3fdb2f.png)
您最近一年使用:0次
2023-10-17更新
|
227次组卷
|
2卷引用:重庆市第十一中学校2023-2024学年高一上学期10月月考数学试题
名校
5 . 如图;在三棱柱中;侧面
为矩形.
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be3cba251ffb7b7959d59aff7dd07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b8771e5813d081e1da7acca1ced4947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0230773e811af6aed85f7dc3f6d57fa.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cfa5b176fd1316fb676bbee21cc5f02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ffed75a3a7b15c0eba70e460d326bd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a10217f7b3ff5ab74c27a0e62debc2ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13779894af95274a6a3158907dc8bfd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926d1308d5db144e31b4d0211c63ef52.png)
您最近一年使用:0次
6 . 如图,边长为4的正方形ABCD所在平面与正三角形
所在平面互相垂直,Q为
的中点.
(1)求证:
;
(2)在线段
上是否存在一点N,使得平面
平面
,若存在,试指出点N的位置,并证明你的结论,若不存在,请说明理由;
(3)求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/7/d4b6912b-37a1-4839-be29-536c27f6f9a9.png?resizew=185)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960f6430bff0919c41a9647a5e511928.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a74d65b2c8e7c219c25d2d7cd549c30b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c51c4a1148587943fe9ba210f6141ee.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61a42adb674d8c2ae066b0a9e465cd9e.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,已知四边形ABCD是平行四边形,点P是平面ABCD外一点,M是PC的中点,在DM上取一点G,过G和AP作平面交平面BDM于GH,H在BD上.
![](https://img.xkw.com/dksih/QBM/2022/4/23/2964390428270592/2965851709530112/STEM/a424408b-2cef-4a24-ba99-dbff1e721d3b.png?resizew=241)
(1)证明:
;
(2)若AB的中点为N,求证:
平面APD.
![](https://img.xkw.com/dksih/QBM/2022/4/23/2964390428270592/2965851709530112/STEM/a424408b-2cef-4a24-ba99-dbff1e721d3b.png?resizew=241)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b364dd4066ce0c2a18c9771e9021769f.png)
(2)若AB的中点为N,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d2bbf2309b4ff8599f57bca4203e90.png)
您最近一年使用:0次
2022-04-25更新
|
2253次组卷
|
4卷引用:重庆市第八中学校2021-2022学年高一下学期期中数学试题
8 . 已知
.
(1)试比较a与b的大小,并证明你的结论;
(2)求证:对任意正数x,y以a,b,c为三边可构成三角形的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eccdb75ef09710f647f0c63ebe14830.png)
(1)试比较a与b的大小,并证明你的结论;
(2)求证:对任意正数x,y以a,b,c为三边可构成三角形的充要条件是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7564582f840149d802de3adf3a1ae67b.png)
您最近一年使用:0次
9 . 已知等边
和等腰
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/3b21bf14-7e13-406f-bec0-24a361ad8888.png?resizew=463)
(1)如图①,点D在BC上,点E在AB上,P是BE的中点,连接AD,PD,求证:
;
(2)如图②,点D在
内部,点E在
外部,P是BE的中点,连接AD、PD,则(1)中的结论是否仍然成立?若成立,请给出证明;若不成立,请说明理由;
(3)如图③,若点D在
内部,点E和点B重合,点P在BC下方,且
为定值,当PD最大时,请直接写出
的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df34369163e511f14028168cb0b21186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f4a098e98e74db40a5aa08eba09a46f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/3b21bf14-7e13-406f-bec0-24a361ad8888.png?resizew=463)
(1)如图①,点D在BC上,点E在AB上,P是BE的中点,连接AD,PD,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/275a94c3e3aa85acb13634aa0b03aae2.png)
(2)如图②,点D在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(3)如图③,若点D在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4d1d99eab930cef884e01b97d4d56f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0433f8116768b42642a7f7e5977ce6.png)
您最近一年使用:0次
名校
10 . 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