如图,正方形ABCD的边长为4,E为AB的中点,将△ADE沿直线DE折叠后,点A落在点F处,DF交对角线AC于G,则FG的长是________ .
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/16/a96483ee-3342-483e-a995-010558ac693f.png?resizew=122)
2020·江苏无锡·一模 查看更多[3]
2020年江苏省宜兴市九年级一模数学试题江苏省沭阳县修远中学2019-2020学年九年级下学期第三次月考数学试题(已下线)专题27.29 相似三角形折叠问题(巩固篇)(专项练习)-2021-2022学年九年级数学下册基础知识专项讲练(人教版)
更新时间:2020-05-15 08:47:29
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(0.15)
【推荐1】如图,
为线段
上一动点(不与点
,
重合),在
同侧分别作等边
和等边
,
与
交于点
,
与
交于点
,
与
交于点
,连接
,
,以下五个结论:①
;②
;③
;④
;⑤
平分
.一定成立的结论有___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0914b68f106a912420705b2f3928ca42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252053b853152bd294a8315debd00b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f80f699558ff62a31152df321b064f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7cea21be341341c2a8ed360e04e87ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701f3b0e2bedfe5195443459072d798e.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/0fc5c19ac440746be97d8b46af5d288a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60e5c088a90d0f4052fc92dd9b7addf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a58293ee5b64497b2fe03f5328fe36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b48674c0491428407735c6632bd5b3b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3f153b6d02a73f686181fe18f3a74c4.png)
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【推荐2】如图, 在
中,
,
,
平分
交
于点
,点E为
上一动点,点
是
上一动点,连接
,以
为斜边向上构造等腰
,延长
交
于
, 连接
, 则 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3751d39d8d08a0d485d75de410cb4aa8.png)
_______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f89deb952f57f4b3fa4887b098b7b91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a24f4190852ceada63342b51b7652a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ab38edd490bae33ec5fbf051c3d612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3751d39d8d08a0d485d75de410cb4aa8.png)
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解题方法
【推荐1】如图,在正方形
中,
.
为对角线
的延长线上一点,
为线段
的中点,
,连接
.已知
,下列说法正确的是______ .(将正确答案的序号填写下来)
①
;②
;③
;④
;⑤若
点为线段
上一动点,当
时,
.
![](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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb91cb9a5a14169845d700fbd95890ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfe31cb2315de7a5300d3efae202e2b6.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b2f883a2a2e0ccc5089fa9f0661e340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/793e03b60fc5ac445d6d44c508e7e73e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9d7b185c499b6bd81f57121f59fb930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ced64b8555b7f3a08faff110c4d15b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d09f17b41174377702f70bc27d10c95a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9ea44e59b1b5f61a5889790cc29d3d.png)
![](https://img.xkw.com/dksih/QBM/2021/5/10/2718155754766336/2786106582319104/STEM/f249101a-e59b-4306-884f-eae978514cce.png)
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【推荐2】如图,
,
,
……在直线上
,
,
,
……在直线上
,
,四边形
为正方形,则四边形
的面积是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2857fac4963b129d99e79dcb3e13d295.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eaf7f1dcb47eb2eee90a687f3a1327f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe6df581fd5dbe1c3de85000caf36186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe6df581fd5dbe1c3de85000caf36186.png)
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【推荐1】
中,
,
,
,折叠
,使点
落在
边上的点
处,折痕
交
于点
,当点
由
向
连续移动过程中,点
经过的路径长记为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ca90e8a784f990c4097eec9219908d.png)
________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a974750a97ff0cb67d19e845b24a929.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cedd51383f8f047f565191b128cec637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1682d306c38087d9e6f7efb9cec596a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05d35d8d8bb0dc17f2f86fe5b230a2b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ca90e8a784f990c4097eec9219908d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a974750a97ff0cb67d19e845b24a929.png)
![](https://img.xkw.com/dksih/QBM/2021/3/16/2679209160499200/2679304135860224/STEM/74389ecd-4df6-4d4b-a45c-b6a8c38f7403.png?resizew=141)
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【推荐2】在矩形ABCD中,AD=8,AB=6,点E为射线DC上一个动点,把△ADE沿AE折叠,使点D落在点F处,若△CEF为直角三角形时,DE的长为______ .
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/16/0d0abb72-26a1-426b-8973-5fd52fd0530c.png?resizew=121)
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【推荐1】如图1,在正方形
中,点E为边
上的一个动点,边
沿
从顶点A出发,向点C平移得到
,连接
,
.设
,
,y关于x的函数图像如题17图2所示,图像经过点
,则图像最低点的横坐标是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ffe9e537a3de08dce8e711ee378001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fff390ac740e3181d476c88616af746b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596329fc40501003d07aea445d4379eb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/aa38daf8-3c4e-4d36-a793-2b2bd966c62f.png?resizew=276)
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【推荐2】如图1是一款多功能儿童餐椅,有坐和躺两种模式,图2是它的横截面示意图,已知脚架
cm,脚垫B,C两点之间的距离为80cm,靠背
cm,分离式餐盘AQ与B,C所在直线平行,固定支撑杆AE平分∠BAC,坐垫EG与AC交于点F,且
cm,脚踏GH始终与AC保持平行,当调到坐式时,
,则此时点D到AQ的距离为______ cm,当调到躺式时,坐垫EG会沿EF方向平移,从点E恰好移动到EF的中点
,GH移动到
,靠背DE向下调整到
,此时
,则点D向下调整的高度为______ cm.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/16/95c0df87-49fa-47be-8c24-f095905706f7.png?resizew=132)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b5f64c51dc1f5ea0a838f066f7d2cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357f980f116fccfa82ba6d4cf62430a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bf004991d64ec5d7de18a9f5bd980fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105068b25f5a63af32f4082cfe08691e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d3db8904d646da962dad4f206ac17b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f23c76692342e0cf0e026b7b9c9432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08f047e38afb66e44eaac8e7a15853b6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/16/95c0df87-49fa-47be-8c24-f095905706f7.png?resizew=132)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/16/fc4c45a6-472b-4f6f-a905-4c35bbc66495.png?resizew=176)
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