1 . 求证:三角形的中位线平行于三角形的第三边,并且等于第三边的一半.
已知:如图,点
、
分别是
的边
、
的中点,连接
.
求证:
,且
.
(要求:尺规作图画出
点和
点,只保留作图痕迹,不写作法)
已知:如图,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c65edad25ddd666cdce0d7e5afefc9.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/e6e490f703eb6c9bb1278c78ebc2d661.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c436f108fd4921dae15ecff19270237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/950e82a0f9712457f2dd9f8a93f8a217.png)
(要求:尺规作图画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/9/05c4409c-d662-4a90-b5e0-1c07e6586b7f.png?resizew=118)
您最近一年使用:0次
2023-01-07更新
|
894次组卷
|
9卷引用:第4章 平行四边形(B卷·能力提升练)-【单元测试】2022-2023学年八年级数学下册分层训练AB卷(浙教版)
(已下线)第4章 平行四边形(B卷·能力提升练)-【单元测试】2022-2023学年八年级数学下册分层训练AB卷(浙教版)山东省淄博市张店区第九中学2022-2023学年八年级上学期期末数学试题(已下线)平行四边形与多边形01技法提练(已下线)专题9.26 三角形的中位线(巩固篇)(专项练习)-2022-2023学年八年级数学下册基础知识专项讲练(苏科版)(已下线)专题9.24 三角形的中位线(知识讲解)-2022-2023学年八年级数学下册基础知识专项讲练(苏科版)(已下线)第二节 尺规作图01技法提练青岛版八年级下册第6章平行四边形单元测试数学试题2022年福建省福州市福建师大附中中考模拟数学试题山东省淄博市高青县第六中学2023-2024学年九年级上学期期末数学试题
2 . 如图,已知
的面积为12,结合尺规作图痕迹所提供的条件可知,
的面积为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9524e3810e06dc781285f1289e75d653.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/11/c85755c0-2fda-45bd-8a6d-74249935349a.png?resizew=155)
您最近一年使用:0次
2023-05-04更新
|
129次组卷
|
3卷引用:2023年浙江省嘉兴市桐乡市中考一模数学试题
2023年浙江省嘉兴市桐乡市中考一模数学试题2023年浙江省嘉兴市海盐县一模数学试题(已下线)专题4.29 相似三角形的性质(分层练习)(提升练)-2023-2024学年九年级数学上册基础知识专项突破讲与练(北师大版)
3 . 如图,在正方形
中,点M在
边上,点N在正方形
外部,且满足
,
,连接
,
,取
的中点E,连接
,
,交于F点.
(1)依题意补全图形,并求证:
;
(2)设
,当点M是
的中点时,求
的长;
(3)设
,若点M沿着线段
从点C运动到点D,则在该运动过程中,线段
所扫过的面积为多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c447ca190f5168a07befbbfa8471ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25be6617d61a7cb5a88b0d680b252b10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/23/f14ab534-807d-46d3-8de7-a6547f86c7d0.png?resizew=118)
(1)依题意补全图形,并求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b8e8956faa2abfb725ce10006082bb.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.png)
您最近一年使用:0次
2023-10-20更新
|
23次组卷
|
2卷引用:浙江省绍兴市秋瑾中学2023-2024学年八年级上学期学科课堂作业(二)数学试题
2024八年级下·浙江·专题练习
4 . 如图,四边形
是平行四边形,
,
,点
是
的中点,点
是
延长线上一点,连接
.
.求证:
.
(2)在(1)的条件下,若
的延长线与
交于点
,试判断四边形
是否为平行四边形,并证明你的结论(请补全图形,再解答)
(3)若
,
与
垂直吗?若垂直,请给予证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc13fe21e64d9b45614ed43be847904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35333abd7f02d663d15251bc5cbbf921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e1e2732f6ae805698f94cc65f14d98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a3f5d73bae2ab3a31c353d38382d25.png)
(2)在(1)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2319a01218514917e446dfc807a625ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82d4c92b24cb675c2aa0d0f80abc59e9.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a3f5d73bae2ab3a31c353d38382d25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
您最近一年使用:0次
5 . 如图,四边形
是平行四边形,
,
,点
是
的中点,点
是
延长线上一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/15/95b581eb-8cea-4ee6-b212-aec2bfe5d2d6.png?resizew=150)
(1)连接
,求证:
.
(2)若
.求证:
.
(3)在(2)的条件下,若
的延长线与
交于点
,试判断四边形
是否为平行四边形
并证明你的结论(请补全图形,再解答)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc13fe21e64d9b45614ed43be847904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35333abd7f02d663d15251bc5cbbf921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/15/95b581eb-8cea-4ee6-b212-aec2bfe5d2d6.png?resizew=150)
(1)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de2c0c8cf35a26a344e9bd19350ee77d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e1e2732f6ae805698f94cc65f14d98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a3f5d73bae2ab3a31c353d38382d25.png)
(3)在(2)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2319a01218514917e446dfc807a625ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82d4c92b24cb675c2aa0d0f80abc59e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
您最近一年使用:0次
名校
6 . 如图1,在
中,
,D是
的中点,点E在线段
上,连结
,作
交直线
于点F,连结
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/18/5046926d-ae2e-4e32-b86e-cd06a349bec5.png?resizew=453)
(1)【初步尝试】
如图2,当
,线段
的长度是 ,线段
的长度是 .
(2)【结论探究】
如图1,小宁猜想“
”,但她未能想出证明思路,小波介绍了添加辅助线的方法,如下表所示,请帮小宁完成证明.
(3)【拓展应用】
如图3,当点E在线段
的延长线上时,连结
,作
交直线
于点F,连结
.请补全图形,并求出当
时,线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b51f6c3470c2a09c87776c1b52f3a7d.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/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c175c239742c7ba8fd67a6d5f99cb1b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/18/5046926d-ae2e-4e32-b86e-cd06a349bec5.png?resizew=453)
(1)【初步尝试】
如图2,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070bc896d35495237fd65576e9b6f88e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
(2)【结论探究】
如图1,小宁猜想“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096ac1e18631f5fdc08d1323661cf4a2.png)
如图,延长![]() ![]() ![]() ![]() ![]() |
如图3,当点E在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c175c239742c7ba8fd67a6d5f99cb1b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b0393ce62b24aa5f9b740d4cc6743b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
您最近一年使用:0次
2023-02-17更新
|
266次组卷
|
2卷引用:浙江省宁波市东钱湖、宋诏桥学校等2022-2023学年八年级上学期期末联考数学试题
7 . 如图,在等边
中,
,点E,F分别为AB,BC的中点,点P从点C出发沿CA的方向运动,到点A停止运动,作线PF,记
,点E到直线PF的距离
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/26/bb176a5c-3351-4129-a34e-ef5ec64d635a.png?resizew=205)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/26/d5c955c6-fa76-4134-834a-ef4c89bb15dc.png?resizew=205)
(1)按照下表中x的值补填完整表格(填准确值):
(2)在坐标系中描出补全后的表中各组数值所对应的点
,用光滑曲线连接;并回答变量y是x的函数吗?为什么?
(3)根据上述信息回答:当x在什么范围内时,y随x的增大而减小?当x取何值时,y的值最大,最大值是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75369931b4a665aa92fba4a28136a8da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be99a73b1607c63b9a82cfa00b81bb9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/26/bb176a5c-3351-4129-a34e-ef5ec64d635a.png?resizew=205)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/26/d5c955c6-fa76-4134-834a-ef4c89bb15dc.png?resizew=205)
(1)按照下表中x的值补填完整表格(填准确值):
x | 0 | 0.5 | 0.75 | 1 | 1.5 | 2 | 2.5 | 3 | 4 |
y | 1.92 | 1.98 | 1.92 | 1.73 | 1.51 | 1.31 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
(3)根据上述信息回答:当x在什么范围内时,y随x的增大而减小?当x取何值时,y的值最大,最大值是多少?
您最近一年使用:0次
8 . 如图是5×5的方格纸,点A,B,C都在格点上,按要求作图.
(2)在图2中仅用无刻度的直尺,作出
的中位线MN使得M在AB上,N在AC上.(保留作图痕迹,不写作法).
(2)在图2中仅用无刻度的直尺,作出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
9 . 图
、图
均是
的正方形网格,每个小正方形的边长均为
,小正方形的顶点称为格点,点
,
,
,
均在格点上,用无刻度的直尺在给定的网格中按要求画图.
,在
上找一点
,连接
,使
;
(2)如图
,在
上找一点
,连接
,使
.(此小题保留作图痕迹)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52826bd7b435a231c6eb5b79fbf7c5be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c6e7c025362c46a64a8956761f08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331799e8261c25cb7e714b02c85dd044.png)
(2)如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a679040c4d556723e482bacbab41356d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/886988c5e3c0a7cea040ccefad874d37.png)
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2024-06-02更新
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106次组卷
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2卷引用:2024年浙江省台州市路桥区中考数学二模试题
10 . 如图,正方形
,矩形
并排放置,
.请用一把无刻度直尺完成下列作图(保留作图痕迹).
中点G;
(2)在图2的边
上找点
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d70fb53a3bc46be3e6365f5ed26496.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae9c17688aff386158eecd10f991131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)在图2的边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ea2d54135d294452ab874753cc71e6.png)
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2024-01-28更新
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64次组卷
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4卷引用:浙江省浙派·振兴联盟2023-2024学年九年级上学期期末数学试题
浙江省浙派·振兴联盟2023-2024学年九年级上学期期末数学试题(已下线)专题10 尺规作图(2大易错点分析+21个易错点+易错题通关)-备战2024年中考数学考试易错题(江苏专用)江西省南昌市2023-2024学年八年级下学期期中数学试题(已下线)专题04 矩形、菱形、正方形性质与判定期末真题汇编【八大题型+优选提升题】-备战2023-2024学年八年级数学下学期期末真题分类汇编(人教版)