解题方法
1 . 如图,在正方形ABCD中,DC=8,现将四边形BEGC沿折痕EG(G,E分别在DC,AB边上)折叠,其顶点B,C分别落在边AD上和边DC的上部,其对应点设为F,N点,且FN交DC于M.
特例体验:
(1)当FD=AF时,△FDM的周长是多少?
类比探究:
(2)当FD≠AF≠0时,△FDM的周长会发生变化吗?请证明你的猜想.
拓展延伸:
(3)同样在FD≠AF≠0的条件下,设AF为x,被折起部分(即:四边形FEGN)的面积为S,试用含x的代数式表示S,并问:当x为何值时,S=26?
特例体验:
(1)当FD=AF时,△FDM的周长是多少?
类比探究:
(2)当FD≠AF≠0时,△FDM的周长会发生变化吗?请证明你的猜想.
拓展延伸:
(3)同样在FD≠AF≠0的条件下,设AF为x,被折起部分(即:四边形FEGN)的面积为S,试用含x的代数式表示S,并问:当x为何值时,S=26?
![](https://img.xkw.com/dksih/QBM/2020/5/2/2454045562478592/2456216496660480/STEM/f2b4e9007ee5464396f5ad6ad768094f.png?resizew=156)
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2020-05-05更新
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2卷引用:2020年江西省中等学校招生考试数学模拟试题(二)
名校
2 . 如图1,在
中,∠B=90°,
,点D,E分别是边BC,AC的中点,连接
将
绕点C按顺时针方向旋转,记旋转角为
.
问题发现:
当
时,
_____;
当
时,
_____.
拓展探究:
试判断:当
时,
的大小有无变化?请仅就图2的情况给出证明.
问题解决:
当
旋转至A、D、E三点共线时,直接写出线段BD的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4457aacb176adef9b80531504abc44a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06acd04006658941055e60e7d34ded72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25fe68a3f4ef8f2e36c7af9a848cb155.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94f802946930ef6cfbcb1a9f033a9092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a1486450f300f451e711d2238eaca1a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/21/0dca8cc9-e46a-45f3-b4a9-cac173d15661.png?resizew=591)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1c9ae241fd78126274c65e17990c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e7e8c4e8015bc1a44a89460e1dc0d63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e85ff0230f5ff1ca98728041de9ce18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c650fe55b7603f106c53ca2423451c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddd284be60584dfae454b1a125468947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a31bc7772d4866e42e5d8c601dc08894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
试判断:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcfbe55f659e4b597bb81680b20db4c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a564371003df29c5f9f327d3c5629521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bb89a362c1faf4d0c306eabbb59710.png)
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94f802946930ef6cfbcb1a9f033a9092.png)
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8卷引用:山西省阳泉市盂县2019-2020学年九年级上学期期末数学试题
名校
3 . 问题情境:在
中,
,点
是
的中点,以
为角的顶点作
.
感知易证:(1)如图1,当射线
经过点
时,
交边
于点
.将
从图1中的位置开始,绕点
按逆时针方向旋转,使射线
、
始终分别交边
,
于点
、
,如图2所示,易证
,则有
.
操作探究:(2)如图2,
与
是否相似,若相似,请证明;若不相似,请说明理由;
拓展应用:(3)若
,直接写出当(2)中的旋转角为多少度时,
与
相似.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1563b386f79fc8ca64ad744eff21998.png)
感知易证:(1)如图1,当射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3533837e3d08c461dea031a44e5424d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a54e7b35c73ee578c4d01479ddb74cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3533837e3d08c461dea031a44e5424d.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d197d256d08e323a48d36c14fa24698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a2c04398112c63d9620f607bedb474.png)
操作探究:(2)如图2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3634979dfcebf857b20874dd320d80b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8129a90e6874cdc7c23ca4784aa9da8a.png)
拓展应用:(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11cf7a72a847385a45fd20a8c53cf004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3634979dfcebf857b20874dd320d80b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://img.xkw.com/dksih/QBM/2020/4/10/2438680395857920/2439120809811968/STEM/6e0dd2370638493a99fe73f789027510.png?resizew=402)
您最近一年使用:0次
4 . 如图1,在矩形ABCD中,AB=6,BC=8,点E是边CD上的点,且CE=4,过点E作CD的垂线,并在垂线上截取EF=3,连接CF.将△CEF绕点C按顺时针方向旋转,记旋转角为a.
![](https://img.xkw.com/dksih/QBM/2020/4/2/2432981048500224/2433157588566016/STEM/0656d59a476446e995423a70b8a74816.png?resizew=416)
(1)问题发现
当a=0°时,AF= ,BE= ,
= ;
(2)拓展探究
试判断:当0°≤a°<360°时,
的大小有无变化?请仅就图2的情况给出证明.
(3)问题解决
当△CEF旋转至A,E,F三点共线时,直接写出线段BE的长.
![](https://img.xkw.com/dksih/QBM/2020/4/2/2432981048500224/2433157588566016/STEM/0656d59a476446e995423a70b8a74816.png?resizew=416)
(1)问题发现
当a=0°时,AF= ,BE= ,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a57799d26dbd66e5f21d327787a542e3.png)
(2)拓展探究
试判断:当0°≤a°<360°时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a57799d26dbd66e5f21d327787a542e3.png)
(3)问题解决
当△CEF旋转至A,E,F三点共线时,直接写出线段BE的长.
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2020-04-03更新
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297次组卷
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8卷引用:2019年河南省开封市中考数学二模试卷
2019年河南省开封市中考数学二模试卷(已下线)专题13 击破类比、探究类综合题利器之相似知识-决胜2020年中考数学压轴题全揭秘精品(河南)2019年河南省开封市中招第二次模拟数学试题2020年河南南阳市卧龙区九年级二模数学试题2020年河南省南阳市九年级二模数学试题2020年河南省南阳市宛城区中考二模数学试卷河南省南阳市淅川县2020-2021学年九年级上学期期末数学试题河南省洛阳市偃师市新前程美语学校2022-2023学年九年级上学期12月月考数学试题
5 . “如图1,在Rt△ABC中,∠ACB=90°,CD⊥AB于点D.”这里,根据已学的相似三角形的知识,易证:
=
.在图1这个基本图形的基础上,继续添加条件“如图2,点E是直线AC上一动点,连接DE,过点D作FD⊥ED,交直线BC于点F,设
=
.”
![](https://img.xkw.com/dksih/QBM/2019/12/28/2364731110563840/2368277763604480/STEM/5af1ea1ea95a429c95abc3c461630f8f.png?resizew=489)
(1)探究发现:如图②,若m=n,点E在线段AC上,则
= ;
(2)数学思考:
①如图3,若点E在线段AC上,则
= (用含m,n的代数式表示);
②当点E在直线AC上运动时,①中的结论是否仍然成立?请仅就图4的情形给出证明;
(3)拓展应用:若AC=
,BC=2
,DF=4
,请直接写出CE的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d8e27dbc73e7270cd5c436e1ec346d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78dc4f4584665f0db3d9363784c1683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78dc4f4584665f0db3d9363784c1683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b648defab69faeb6479e952ecc1bfee3.png)
![](https://img.xkw.com/dksih/QBM/2019/12/28/2364731110563840/2368277763604480/STEM/5af1ea1ea95a429c95abc3c461630f8f.png?resizew=489)
(1)探究发现:如图②,若m=n,点E在线段AC上,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59691203308c8d4d0e4657639fabc43c.png)
(2)数学思考:
①如图3,若点E在线段AC上,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59691203308c8d4d0e4657639fabc43c.png)
②当点E在直线AC上运动时,①中的结论是否仍然成立?请仅就图4的情形给出证明;
(3)拓展应用:若AC=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
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2020-01-02更新
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4卷引用:河南省南阳市方城县2019-2020学年九年级上学期期中数学试题
名校
6 . 如图1,在Rt△ABC中,∠C=90°,AC=8,AB=10,D,E两点分别是AC,CB上的点,且CD=6,DE∥AB,将△CDE绕点C顺时针旋转一周,记旋转角为α.
(1)问题发现
①当α=0°时,
=______;
②当α=90°时,
=______.
(2)拓展探究
请你猜想当△CDE在旋转的过程中,
是否发生变化?根据图2证明你的猜想.
(3)问题解决
在将△CDE绕点C顺时针旋转一周的过程中,当AD=2
时,BE=____,此时α=_____.
(1)问题发现
①当α=0°时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9180c2c249f2583751113ea3a674a18.png)
②当α=90°时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9180c2c249f2583751113ea3a674a18.png)
(2)拓展探究
请你猜想当△CDE在旋转的过程中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9180c2c249f2583751113ea3a674a18.png)
(3)问题解决
在将△CDE绕点C顺时针旋转一周的过程中,当AD=2
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50690dab38f4512eb72e18b7f86cf6f6.png)
![](https://img.xkw.com/dksih/QBM/2019/8/14/2268751766462464/2269097876922368/STEM/9281d702-2869-49c7-849d-97a11c90eaba.png?resizew=293)
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2019-08-15更新
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3卷引用:2019年河南省洛阳市中考三模数学试题
2019年河南省洛阳市中考三模数学试题(已下线)专题13 击破类比、探究类综合题利器之相似知识-决胜2020年中考数学压轴题全揭秘精品(河南)河南省洛阳市涧西区东方第二中学2019-2020学年九年级下学期期中数学试题
7 . 在△ABC中,
,AC=4,BC=3,点D是斜边AB的中点. 以点D为顶点作
,射线DM、DN分别交边AC、CB于点E、F.
![](https://img.xkw.com/dksih/QBM/2020/3/15/2426309322129408/2429457600331777/STEM/290f0f0266cb4cd2a7586ce315a8e93c.png?resizew=561)
特例分析:
(1)如图1,若
,不添加辅助线,图1中所有与△ABC相似的三角形为 ,
;
操作探究:
(2)将(1)中的
从图1 的位置开始绕点D按逆时针方向旋转,得到
.如图2,当射线
分别交边
于点
时,求
的值;
拓展延伸:
(3)如图3,
中,
,AC=m,BC=n,点D是斜边AB的中点,以点D为顶点作
,射线
分别交边
的延长线于点
,则
的值为_______________.(用含
的代数式表示,直接回答即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed8f7d3d7043d4b1eb98fc5c4e2fcd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90c4cde2e661d54201bdfe980068e20a.png)
![](https://img.xkw.com/dksih/QBM/2020/3/15/2426309322129408/2429457600331777/STEM/290f0f0266cb4cd2a7586ce315a8e93c.png?resizew=561)
特例分析:
(1)如图1,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d06414d50303a954564eb64235fb448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c0401d394546dcf04cfead7d5b8f97.png)
操作探究:
(2)将(1)中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a54e7b35c73ee578c4d01479ddb74cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591a6c4d152af17480a66fb0a2aef47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3f962cc6c8b902dfff603bbbe43ce3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11863656c0830c8ca56a8f4490153cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a6c56adee2202fe136844c638a6a70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8d8f7a4c1e98dcf0e63c62898f3ed55.png)
拓展延伸:
(3)如图3,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed8f7d3d7043d4b1eb98fc5c4e2fcd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90c4cde2e661d54201bdfe980068e20a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a39e7d661f70964ad5eecaaaf2c432b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11863656c0830c8ca56a8f4490153cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810f9b4c1535bf75de1e31c164ccfe1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0877194ab8760f54c35527177b03ff93.png)
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2020-03-28更新
|
227次组卷
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7卷引用:山西省晋中市2018-2019学年九年级上学期期中数学试题
山西省晋中市2018-2019学年九年级上学期期中数学试题山西省运城2018-2019学年九年级上学期阶段二质量评估数学试题山西省运城市2018-2019学年九年级上学期期中数学试题山西省晋中2018-2019学年九年级上学期阶段二质量评估数学试题(已下线)专题4.44 三角形相似与旋转综合专题(巩固篇)(专项练习)-2022-2023学年九年级数学上册基础知识专项讲练(北师大版)(已下线)专题27.41 相似三角形与旋转综合专题(巩固篇)(专项练习)-2022-2023学年九年级数学下册基础知识专项讲练(人教版)(已下线)专题6.42 相似三角形与旋转综合专题(巩固篇)(专项练习)-2022-2023学年九年级数学下册基础知识专项讲练(苏科版)
8 . 【问题发现】如图1,半圆O的直径AB=10,点P是半圆O上的一个动点,则△PAB的面积最大值是 ;
【问题探究】如图2所示,AB、AC、
是某新区的三条规划路,其中AB=6km,AC=3km,∠BAC=60°,
所对的圆心角为60°.新区管委会想在
路边建物资总站点P,在AB、AC路边分别建物资分站点E、F,即分别在
、线段AB和AC上选取点P、E、F.由于总站工作人员每天要将物资在各物资站点间按P→E→F→P的路径进行运输,因此,要在各物资站点之间规划道路PE、EF和FP.显然,为了快捷环保和节约成本,就要使线段PE、EF、FP之和最短(各物资站点与所在道路之间的距离、路宽均忽略不计).可求得△PEF周长的最小值为 km;
【拓展应用】如图3是某街心花园的一角,在扇形OAB中,∠AOB=90°,OA=12米,在围墙OA和OB上分别有两个入口C和D,且AC=4米,D是OB的中点,出口E在
上.现准备沿CE、DE从入口到出口铺设两条景观小路,在四边形CODE内种花,在剩余区域种草.
①出口E设在距直线OB多远处可以使四边形CODE的面积最大?最大面积是多少?(小路宽度不计)
②已知铺设小路CE所用的普通石材每米的造价是200元,铺设小路DE所用的景观石材每米的造价是400元.
请问:在
上是否存在点E,使铺设小路CE和DE的总造价最低?若存在,求出最低总造价和出口E距直线OB的距离;若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/12/b53108fb-10b8-4443-a88b-3ba9dbdcde57.png?resizew=155)
【问题探究】如图2所示,AB、AC、
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/12/c793fb2d-49bf-4641-8842-9297c70384f0.png?resizew=106)
【拓展应用】如图3是某街心花园的一角,在扇形OAB中,∠AOB=90°,OA=12米,在围墙OA和OB上分别有两个入口C和D,且AC=4米,D是OB的中点,出口E在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
①出口E设在距直线OB多远处可以使四边形CODE的面积最大?最大面积是多少?(小路宽度不计)
②已知铺设小路CE所用的普通石材每米的造价是200元,铺设小路DE所用的景观石材每米的造价是400元.
请问:在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/12/d067d9a4-3613-4dd9-8a93-3b574b893fa5.png?resizew=98)
您最近一年使用:0次
真题
9 . 问题情境:如图1,在正方形ABCD中,E为边BC上一点(不与点B、C重合),垂直于AE的一条直线MN分别交AB、AE、CD于点M、P、N.判断线段DN、MB、EC之间的数量关系,并说明理由.
![](https://img.xkw.com/dksih/QBM/2019/6/18/2228334156029952/2228478978580480/STEM/0f007fe7ab0642ac9567781046574b0c.png?resizew=132)
问题探究:在“问题情境”的基础上,
(1)如图2,若垂足P恰好为AE的中点,连接BD,交MN于点Q,连接EQ,并延长交边AD于点F.求∠AEF的度数;
![](https://img.xkw.com/dksih/QBM/2019/6/18/2228334156029952/2228478978580480/STEM/ebe0d7e6bf8d437c91e0ca3837e3d8f0.png?resizew=134)
(2)如图3,当垂足P在正方形ABCD的对角线BD上时,连接AN,将△APN沿着AN翻折,点P落在点P'处.若正方形ABCD的边长为4 ,AD的中点为S,求P'S的最小值.
![](https://img.xkw.com/dksih/QBM/2019/6/18/2228334156029952/2228478978580480/STEM/dd229c523b4649e3ae92afb0dedd5806.png?resizew=126)
问题拓展:如图4,在边长为4的正方形ABCD中,点M、N分别为边AB、CD上的点,将正方形ABCD沿着MN翻折,使得BC的对应边B'C'恰好经过点A,C'N交AD于点F.分别过点A、F作AG⊥MN,FH⊥MN,垂足分别为G、H.若AG=
,请直接写出FH的长.
![](https://img.xkw.com/dksih/QBM/2019/6/18/2228334156029952/2228478978580480/STEM/0f007fe7ab0642ac9567781046574b0c.png?resizew=132)
问题探究:在“问题情境”的基础上,
(1)如图2,若垂足P恰好为AE的中点,连接BD,交MN于点Q,连接EQ,并延长交边AD于点F.求∠AEF的度数;
![](https://img.xkw.com/dksih/QBM/2019/6/18/2228334156029952/2228478978580480/STEM/ebe0d7e6bf8d437c91e0ca3837e3d8f0.png?resizew=134)
(2)如图3,当垂足P在正方形ABCD的对角线BD上时,连接AN,将△APN沿着AN翻折,点P落在点P'处.若正方形ABCD的边长为4 ,AD的中点为S,求P'S的最小值.
![](https://img.xkw.com/dksih/QBM/2019/6/18/2228334156029952/2228478978580480/STEM/dd229c523b4649e3ae92afb0dedd5806.png?resizew=126)
问题拓展:如图4,在边长为4的正方形ABCD中,点M、N分别为边AB、CD上的点,将正方形ABCD沿着MN翻折,使得BC的对应边B'C'恰好经过点A,C'N交AD于点F.分别过点A、F作AG⊥MN,FH⊥MN,垂足分别为G、H.若AG=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533a7b702ada1dd80123e4041271d521.png)
![](https://img.xkw.com/dksih/QBM/2019/6/18/2228334156029952/2228478978580480/STEM/305416ade8f54068a55b073705a15213.png?resizew=160)
您最近一年使用:0次
2019-06-18更新
|
887次组卷
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7卷引用:江苏省连云港市2019年中考数学试题
江苏省连云港市2019年中考数学试题(已下线)江苏省连云港市2019年中考数学试题人教版八年级正方形培优训练广东省广州市荔湾区第四中学2019-2020学年九年级上学期10月月考数学试题(已下线)专题12 图形的性质之解答题《备战2020年中考真题分类汇编》(江苏省)(已下线)热点专题6 图形折叠问题-《三步冲刺中考·数学》之热点专题冲刺(江苏专用)(已下线)热点专题2 规律探究问题-《三步冲刺中考·数学》之热点专题冲刺(江苏专用)
10 . (1)问题发现:如图1,在等边
中,点
为
边上一动点,
交
于点
,将
绕点
顺时针旋转
得到
,连接
.则
与
的数量关系是_____,
的度数为______.
![](https://img.xkw.com/dksih/QBM/2019/6/11/2223361278779392/2224036911071232/STEM/2666ac835960423483b82c2b6fe74c64.png?resizew=120)
(2)拓展探究:如图2,在
中,
,
,点
为
边上一动点,
交
于点
,当∠ADF=∠ACF=90°时,求
的值.
![](https://img.xkw.com/dksih/QBM/2019/6/11/2223361278779392/2224036911071232/STEM/8839236f21a04200a5226e054c13d381.png?resizew=109)
(3)解决问题:如图3,在
中,
,点
为
的延长线上一点,过点
作
交
的延长线于点
,直接写出当
时
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe7eaf967808dad0a184eeedfa27721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735056c174e8dd7906257a2a50a962a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752fa646a2d9cfca34001748445301c9.png)
![](https://img.xkw.com/dksih/QBM/2019/6/11/2223361278779392/2224036911071232/STEM/2666ac835960423483b82c2b6fe74c64.png?resizew=120)
(2)拓展探究:如图2,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52058d155a05c34f3ee8251bb92b3238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26fdd8e57562ba94e10e7f1d770826d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe7eaf967808dad0a184eeedfa27721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6801c7dff835297ca268b455754e8d02.png)
![](https://img.xkw.com/dksih/QBM/2019/6/11/2223361278779392/2224036911071232/STEM/8839236f21a04200a5226e054c13d381.png?resizew=109)
(3)解决问题:如图3,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b672c4ca5d81ad900ae9718ff4bbafc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe7eaf967808dad0a184eeedfa27721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aaa75dfec8f85471d14617d9d5ed5d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6801c7dff835297ca268b455754e8d02.png)
![](https://img.xkw.com/dksih/QBM/2019/6/11/2223361278779392/2224036911071232/STEM/c6ccdad779034136acc538f4678c44d4.png?resizew=166)
您最近一年使用:0次
2019-06-12更新
|
707次组卷
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4卷引用:试河南省安阳市2019届九年级下学期第一次模拟考试数学试题