1 . 综合与探究
在矩形
中,
,
,
,
是对角线
上的两个动点,点
,
分别从点A,
同时出发,相向而行,速度均为每秒1个单位长度,运动时间为
秒,
,
分别是
,
的中点,连接
,
,
,
.
的形状一定是______(点
,
相遇时除外).
(2)当四边形
为矩形时,请求出
的值.
(3)若点
向点
运动,点
向点
运动,且与点
,
以相同的速度同时出发,当四边形
为菱形时,求
的值.
在矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d649afbddd907f0dfec1420f02f82fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b939af5ba06e279cce39396aaf0fae06.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/60ef95894ceebaf236170e8832dcf7e3.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff5428516bd29c368d0218087b1c6a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.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/91f3956f008cc29ca4bae44a087d5427.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a16f5621716bfef7a056a3f2712feb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b95463a97c60db3250cb641bf6523d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1522a9c3b2466395570c2689a4055584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(2)当四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1522a9c3b2466395570c2689a4055584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/1522a9c3b2466395570c2689a4055584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2 . 综合与实践卜
数学活动∶在综合与实践活动课上,老师让同学们以“三角形纸片的折叠、旋转”为主题开展数学活动,探究线段长度的有关问题.
动手操作:在
中,
,
,
,将三角形纸片
进行以下操作:
第一步∶如图1,将
沿着
进行翻折,使点C与点A重合,然后展开铺平,得到折痕
;
第二步∶如图2,隐去
,将
沿折痕
剪开,然后将
绕点D逆时针方向旋转得到
,点E,C的对应点分别是点F,G,射线
与边
交于点M,(M不与点A重合),与边
交于点N,线段
与
交于点P.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/31/3dd2bb0b-d3c3-4e01-8490-703106d9785c.png?resizew=369)
数学思考:
(1)在图1中,求证∶
;
(2)在图2中,
绕点D旋转的过程中,试判断
与
的数量关系,并证明你的结论;
(3)在
绕点D旋转的过程中,探究下列问题:
①如图3,当
时,
________;
②如图4,当
经过点B时,
________.
数学活动∶在综合与实践活动课上,老师让同学们以“三角形纸片的折叠、旋转”为主题开展数学活动,探究线段长度的有关问题.
动手操作:在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4494a85de0be0b97a69348115aef8513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
第一步∶如图1,将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2689f0ce5ab3467d8214794d8acb2bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
第二步∶如图2,隐去
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2689f0ce5ab3467d8214794d8acb2bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029ad83f1a3262048cba0e650b63e929.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.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/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/31/3dd2bb0b-d3c3-4e01-8490-703106d9785c.png?resizew=369)
数学思考:
(1)在图1中,求证∶
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ff29971ccc633d89832ffa9bd54afa3.png)
(2)在图2中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2689f0ce5ab3467d8214794d8acb2bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce6c0e9de83f2e64ae33609fc08459d.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2689f0ce5ab3467d8214794d8acb2bd6.png)
①如图3,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a95a2a2d3ead86a287255a428997c399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1039601edd7326b628a3201a3d4af948.png)
②如图4,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1039601edd7326b628a3201a3d4af948.png)
您最近一年使用:0次
3 . 眼睛是人类感官中最重要的器官之一,每年的6月6日定为全国爱眼日,小林想要探究自己按照标准护眼姿势读书时书籍应离身体多远,画出如图的侧面示意图,点A为眼睛的位置,A到书籍
的距离
为40cm,
与水平方向夹角
为
,小林在书桌上方的身长
为52cm,且
垂直于水平方向,请你求出小林与书籍底端的水平距离
.(参考数据:
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d598f4a17ac14970ade9f381e9aee970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48cf21017ebe712348fbe500113dbc59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70716b98e77bdcd68512b18f91ccbb21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8fd5213e37e2555db9cc2c12cec7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9585715711c64f7778a59feb4e0d599.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/27/46e3f426-11f3-4f3e-af0e-cc1a45adf2fb.png?resizew=346)
您最近一年使用:0次
2023-09-09更新
|
177次组卷
|
3卷引用:山西省晋城市多校2023-2024学年九年级上学期期末联考数学试题
4 . 综合与探究
中,
,直线
经过点
,过点
作
于点
,过点
作
于点
.求证:
;
(2)模型应用:
①如图2,已知直线
与
轴交于
点,与
轴交于
点,将线段
绕点
逆时针旋转
,得到线段
,过点
作直线,求直线
的函数解析式;
②如图3,长方形
,点
为坐标原点,点
的坐标为
分别在坐标轴上,点
是线段
上动点,已知点
在第一象限,且是直线
上的一点,若
是不以点
为直角顶点的等腰直角三角形,请直接写出所有符合条件的点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d7d287e59b8033ee3c7540707ace3f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c388d0a3f0a8d9fb0b9576d00af225.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/f5c60ab4cdefda079244161bb911a453.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172d93e9195e92d7924c0aea3d4c7eaa.png)
(2)模型应用:
①如图2,已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1d7df623642896d720d6956ed1f0ff6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
②如图3,长方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/607543bb9f55b8a141ed2d6cf0e1a20b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b78366b6ccaef4996fef7559b8fd3df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/694033aa4e20853cf10f33c870007047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7fbd6b9f85c086ac95562fe45e8d969.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
5 . 综合与实践:
问题情景:如图,在
中,
为对角线
,
的交点,
,
,
,
为
上一动点,连接
并延长交
于点
.
独立思考:(1)当
时,求
的度数;
实践探究:(2)当四边形
为平行四边形时,求
的长;
问题解决:(3)当点
在
的垂直平分线上时,直接写出
的长.
问题情景:如图,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650c6c818df102a83ce5159e3208d01a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feda722a8a8f4b6a84d9ea614e4e8de7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
独立思考:(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d84733f9dc908ceb11459cc2aed580ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05805b7d1de800f3446ea176a9e00b64.png)
实践探究:(2)当四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bddc68ed03fe7fd1fe30a5e626ba435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
问题解决:(3)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/20/c576cd26-d1e8-4241-bb51-a65ff3e617a4.jpg?resizew=333)
您最近一年使用:0次
2023-08-12更新
|
88次组卷
|
3卷引用:山西省运城市2022—2023学年八年级下学期期末数学试题
山西省运城市2022—2023学年八年级下学期期末数学试题山西省清徐县县城第二初级中学校2022--2023学年八年级下学期期末数学试题(已下线)专题18.13 矩形(分层练习)(提升练)-2023-2024学年八年级数学下册基础知识专项突破讲与练(人教版)
6 . 综合与实践
问题情境:在
中,
.点
在
斜边
上运动,过点
作射线
,分别与边
交于点
.
猜想证明:
(1)当点
在
斜边
的中点处时,
①如图(1),在
旋转过程中,当点
时,
与
的数量关系是______,
_______.
②当
旋转到如图②所示的位置时,
的值是否发生变化?若不变,请证明;若变化,请说明理由.
③如图③,在
旋转过程中,当
时,直接写出线段
的长_______;
类比探究
(2)当点
在
斜边
上运动时,
①如图④,当点
运动到
时,
_______;
②如图⑤,连接
,当
是等腰三角形时,求
的长.
问题情境:在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d0c819e913ae45d87a1898257e8e6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.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/5be6e0c4c7e268084a0523f54fbe9f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
猜想证明:
(1)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/31/7a619122-13c8-426e-959b-894b7bf82975.png?resizew=698)
①如图(1),在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46060ff16376f584eb554e09686ab703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/824938c27f63ba9b36eaea6cdd389e6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3525ddc5153fada64eaf14e50b536542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e064e7a02d1db4f5269e7a512c23baf.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46060ff16376f584eb554e09686ab703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fcc76f6c07ce7e0bc75653ea0351526.png)
③如图③,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46060ff16376f584eb554e09686ab703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b38bbd93669765af69d7bb0049e2819b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
类比探究
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
①如图④,当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5461da7d3ccd8ae644157361962a8693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e064e7a02d1db4f5269e7a512c23baf.png)
②如图⑤,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/129f1d6567bef09b00b7f37894e6dba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
您最近一年使用:0次
7 . 综合与探究
如图,在平面直角坐标系中,直线
与
轴,
轴分别交于点
,
,直线
与
轴,
轴分别交于点
,
,两条直线交于点
,且点
的横坐标为
;连接
.
的函数解析式;
(2)求
的面积;
(3)若点
在直线
上,
为坐标平面内任意一点,试探究:是否存在以点
,
,
,
为顶点的四边形是矩形?若存在,请直接写出点
的坐标;若不存在,请说明理由.
如图,在平面直角坐标系中,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1e6043df5ef7c948946ef56eca4b1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a01e2e3d40112fdeeb464f81eaac1c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77cb0a28d72b7e7eacc877e97bc7ff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7294f5ae2a24ff42e84cd9773b2a7287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/a0ed1ec316bc54c37c4286c208f55667.png)
您最近一年使用:0次
2023-07-12更新
|
131次组卷
|
4卷引用:山西省吕梁市交口县2022-2023学年八年级下学期期末数学试题
山西省吕梁市交口县2022-2023学年八年级下学期期末数学试题山西省吕梁市吕梁市三校、离石区六校2022-2023学年八年级下学期6月期末数学试题 山东省济南市市中区2023-2024学年九年级上学期开学数学试题(已下线)专题19.18 一次函数与方程、不等式(分层练习)(提升练)-2023-2024学年八年级数学下册基础知识专项突破讲与练(人教版)
8 . 如图,已知等边
的边长为
,点
是
边上的一个动点(与点A、B不重合),直线
是经过点
的一条直线,把
沿直线l折叠,点B的对应点是点
.
(1)基础图形:如图1,当
时,若点
恰好在
边上,求
的长度;
(2)模型变式:如图2,当
时,若直线
,则
的长度为______;
(3)动态探究:如图3,点
在
边上运动过程中,点
到直线
的距离为
.
如果直线
始终垂直于
,那么
的值是否变化?若变化,求出
的变化范围;若不变化,求出
的值;
当
时,请直接写出在直线
的变化过程中,
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/17/d35c2fec-f987-4cea-b94b-47e3a65bd3ca.png?resizew=626)
(1)基础图形:如图1,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b336e518ac4ff04c6c26e4b8a15844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943712a5e96b16cc15d775cc4687237e.png)
(2)模型变式:如图2,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ce0586aafd9bf4fb7e1be082624afc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7db6f7222557290dc8d38bfa661608a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
(3)动态探究:如图3,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1c9ae241fd78126274c65e17990c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c650fe55b7603f106c53ca2423451c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f71f070c1aa967a945113735322fae18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
解题方法
9 . 综合与实践
问题情境:
矩形ABCD中,AB=2,∠ADB=30°,将△BCD沿着对角线BD所在的直线平移,得到△B′C′D′,连接AB′,DC′.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/30/8e42733a-f530-42f7-8cd7-3a1e5a2cc90b.png?resizew=670)
操作探究:
(1)如图1,当△BCD沿射线BD的方向平移时,请判断AB′与DC′的长度有何关系?并说明理由;
(2)如图2,当△BCD沿射线DB的方向平移时,四边形AB′C′D能成为菱形吗?若能,求出平移的距离;若不能,说明理由;
(3)当△BCD平移距离为2时,请你在备用图中画出平移后的图形(除图2),并提出一个问题,直接写出结论.
问题情境:
矩形ABCD中,AB=2,∠ADB=30°,将△BCD沿着对角线BD所在的直线平移,得到△B′C′D′,连接AB′,DC′.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/30/8e42733a-f530-42f7-8cd7-3a1e5a2cc90b.png?resizew=670)
操作探究:
(1)如图1,当△BCD沿射线BD的方向平移时,请判断AB′与DC′的长度有何关系?并说明理由;
(2)如图2,当△BCD沿射线DB的方向平移时,四边形AB′C′D能成为菱形吗?若能,求出平移的距离;若不能,说明理由;
(3)当△BCD平移距离为2时,请你在备用图中画出平移后的图形(除图2),并提出一个问题,直接写出结论.
您最近一年使用:0次
10 . 阅读以下材料,并按要求完成相应的任务:
三角形中位线定理的证明
如图1,△ABC中,点D,E分别是AB,AC的中点,连接DE,像DE这样,连接三角形两边的中点的线段叫做三角形的中位线.求证:DE∥BC,且DE=
BC.
证明:如图2,延长DE到点F,使EF=DE,连接FC,DC,AF.
∵AE=EC,DE=EF,
∴四边形ADCF是平行四边形(依据1).
∴CF//DA,CF=DA.
∵DA=BD,
∴CF//BD,CF=BD.
∴四边形DBCF是平行四边形(依据2).
∴CF//BC,CF=BC.
∵DE=
DF,
∴DE∥BC,且DE=
BC.
归纳总结:
上述证明过程中运用了“倍长线段法”,也有人称材料中的方法为“倍长法”(延长了三角形中位线的一倍),该方法是解决初中数学几何题的一种常用方法.
任务(1)
上述材料证明过程中的“依据1”是指: ;
“依据2”是指: ;
类比探究
数学学习小组发现还可以用“倍长线段法”证明定理:直角三角形斜边上的中线等于斜边的一半.
已知:如图3,在Rt△ACB中,∠ACB=90°,E为AB边的中点,求证:CE=
AB.
证明:延长CE到点F,使EF=CE,连接BF,AF,如图4.
任务(2)请将证明过程补充完整.
三角形中位线定理的证明
如图1,△ABC中,点D,E分别是AB,AC的中点,连接DE,像DE这样,连接三角形两边的中点的线段叫做三角形的中位线.求证:DE∥BC,且DE=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/7/5f579953-7e88-4c7a-8cb2-7d944b0dfde0.png?resizew=264)
证明:如图2,延长DE到点F,使EF=DE,连接FC,DC,AF.
∵AE=EC,DE=EF,
∴四边形ADCF是平行四边形(依据1).
∴CF//DA,CF=DA.
∵DA=BD,
∴CF//BD,CF=BD.
∴四边形DBCF是平行四边形(依据2).
∴CF//BC,CF=BC.
∵DE=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
∴DE∥BC,且DE=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
归纳总结:
上述证明过程中运用了“倍长线段法”,也有人称材料中的方法为“倍长法”(延长了三角形中位线的一倍),该方法是解决初中数学几何题的一种常用方法.
任务(1)
上述材料证明过程中的“依据1”是指: ;
“依据2”是指: ;
类比探究
数学学习小组发现还可以用“倍长线段法”证明定理:直角三角形斜边上的中线等于斜边的一半.
已知:如图3,在Rt△ACB中,∠ACB=90°,E为AB边的中点,求证:CE=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
证明:延长CE到点F,使EF=CE,连接BF,AF,如图4.
任务(2)请将证明过程补充完整.
您最近一年使用:0次
2021-08-30更新
|
361次组卷
|
3卷引用:山西省大同市2020-2021学年八年级下学期期末数学试题