1 . 如图,直线
与双曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86dbcb009fb9e25cc1d3f447c89fa482.png)
交于
、
两点,连接
、
,
轴于
,
轴于
,设
,
的解析式分别为
,
,现有以下结论:①
;②
;③若
,则
;④
有最小值.其中正确的是 _____ .(写出所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318db708626c4e9d975e0c8c4e87acf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86dbcb009fb9e25cc1d3f447c89fa482.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab03556c333ab0b55fe86c937b2a5763.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/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41075397f8e19313eaed03814276fa32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff86ca2de3dd3592e013ff0e43b472e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1447dbe580ac5c825776995118e75acf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d4f20f4d98141613ff5dd7c37b55c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17bda892497cea43df67db57b4e2a07a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4784d5c6c99f2d18699f1ece85d70c8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5784ea22dbd90af6cdceae43f80a22e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0121adef8281a61254804b7fba49c8f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/12/ecd2c816-974e-4731-94ec-7c6dd014b013.png?resizew=184)
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6卷引用:2021年福建省九年级下学期百校联考(诊断卷二)数学试题
2021年福建省九年级下学期百校联考(诊断卷二)数学试题(已下线)第11章 反比例函数(A卷·知识通关练) -【单元测试】2022-2023学年八年级数学下册分层训练AB卷(苏科版)(已下线)专题11.20 反比例函数和一次函数综合(培优篇)(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11.28 反比例函数(最值问题)(培优篇)(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6.28 反比例函数(最值问题)(培优篇)(专项练习)-2022-2023学年八年级数学下册基础知识专项讲练(浙教版)(已下线)专题6.20 反比例函数和一次函数综合(培优篇)(专项练习)-2022-2023学年八年级数学下册基础知识专项讲练(浙教版)
2 . (1)已知:如图,AD、BC相交于点O,
,
.求证:
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/11/351c9b2f-a7c4-4ce9-8b67-a6948c3036a7.png?resizew=205)
(2)如图,方格纸中每个小正方形的边长都是单位1,△ABC在平面直角坐标系中的位置如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/11/1e3985c3-181e-4df4-aee0-ff54132e2cb4.png?resizew=246)
①将△ABC向右平移4个单位后,得到
,画出
,直接写出点
的坐标;
②画出
关于x轴的对称图形
,求出四边形
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c35c43d90814396ff06336fa45e9650.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c220eadc312101e2fb89dfe920f7b30d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/11/351c9b2f-a7c4-4ce9-8b67-a6948c3036a7.png?resizew=205)
(2)如图,方格纸中每个小正方形的边长都是单位1,△ABC在平面直角坐标系中的位置如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/11/1e3985c3-181e-4df4-aee0-ff54132e2cb4.png?resizew=246)
①将△ABC向右平移4个单位后,得到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
②画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828dc8dc7259c510b6d63abf40f60e90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ba5b68970e893fbe2df2bc01a164c67.png)
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3 . 如图,四边形
中,
,
,
,
,则
的长是( )
![](https://img.xkw.com/dksih/QBM/2022/2/21/2921406885224448/2963483392622592/STEM/e9358cbb6b4a46829135bc2be642e208.png?resizew=137)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e1f53419e397ec94fd40c97a0fe2a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c897a54f2e36bc4b52fba74b41c89d2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3798a74058ec4bc40b6d9b5d268c359b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc5df62e8ac9c74a46462519b95479a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://img.xkw.com/dksih/QBM/2022/2/21/2921406885224448/2963483392622592/STEM/e9358cbb6b4a46829135bc2be642e208.png?resizew=137)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 如图,在△ABE和△CDF中,点C、E、F、B在同一直线上,BF=CE,若AB∥CD,∠A=∠D.求证:AB=CD.
![](https://img.xkw.com/dksih/QBM/2021/12/28/2884366274879488/2948297999179776/STEM/80a9dedb-3ff9-49d0-9f98-032cdc531de4.png?resizew=221)
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10卷引用:2021年福建省厦门市湖滨中学九年级中考二模试题
2021年福建省厦门市湖滨中学九年级中考二模试题广东省广州市天河区汇景实验学校2021-2022学年九年级上学期期中数学试题2广东省广州市天河区汇景实验学校2021-2022学年九年级上学期期中数学试题1吉林省长春市二道区2021-2022学年八年级上学期期末数学试题吉林省长春市二道区2021-2022学年八年级上学期期末数学试题2(已下线)考点22 全等三角形-备战2022年中考数学一轮复习考点帮(全国通用)江苏省淮安市洪泽外国语中学集团2021-2022学年九年级下学期随堂练习(一)数学试题山东省济南市市中区2021-2022学年七年级下学期期末数学试题广东省广州市华南师范大学附属中学2021~2022学年九年级数学上学期第一次月考模拟考试卷2 广东省韶关市翁源县2023-2024学年八年级上学期期中数学试题
名校
5 . 如图,直线AB、CD相交于点E,E是AB的中点,AD∥BC.
求证:AD=BC.
求证:AD=BC.
![](https://img.xkw.com/dksih/QBM/2022/3/12/2934633659465728/2936056791056384/STEM/770696e1ae334c4ab2574e0bb64428fb.png?resizew=140)
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3卷引用:2021年福建省厦门市思明区大同中学中考数学模拟试题
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6 . 如图,若点O是正六边形ABCDEF的中心,
,且角的两边分别交六边形的边AB、EF于M、N两点.若多边形AMONF的面积为
,则正六边形ABCDEF的外接圆的面积是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac144685e50009fa7c9233d85e8bd85b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://img.xkw.com/dksih/QBM/2021/6/22/2748618435018752/2799650553192448/STEM/3b52c4fc-cb29-410b-a64b-4145903496bd.png)
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7 . 如图,在
中,
于点
,
于点
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3f5dc11efe60b4fd9a13b1d6b83842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b62ce0cbffa4758c7a0e6fb7ca4d24e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92034dd2bb9480b18709d01153467f8f.png)
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3卷引用:2021年福建省泉州市第五中学九年级中考模拟考试数学试题
名校
解题方法
8 . 如图1,在正方形ABCD中,边长为2a,点E是AB边上的一个动点(点E与点A,B不重合),连接CE,过点B作BF⊥CE于点G,交AD于点F.
(1)求证:AF=BE;
(2)如图2,当点E运动到AB中点时,连接DG,求证:DG=2a;
(3)如图3,在(2)的条件下,过点C作CM⊥DG于点H,分别交AD,BF于点M,N,求
的值.
(1)求证:AF=BE;
(2)如图2,当点E运动到AB中点时,连接DG,求证:DG=2a;
(3)如图3,在(2)的条件下,过点C作CM⊥DG于点H,分别交AD,BF于点M,N,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7257b25ee15cdb509fb4a9e84113c843.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/788387a9-a8c9-434f-8682-eaeaeeba2e1b.png?resizew=441)
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9 . 如图,四边形
中,
分别是
边上的点,连接
相交于点O.若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37af8da97b7487df7840c29f51ff1924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d93949d8a15aca4e79cedb978590571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bd6557072c6e3f2debbd1df5ef14ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcf2e3236ea30ee2c37928b98041f13a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ce1475f537b4ad21775bfaa16daa0c.png)
![](https://img.xkw.com/dksih/QBM/2021/5/13/2720026460741632/2721596245934080/STEM/a3375a6c-8adf-4499-8707-a3068f5094f2.png)
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4卷引用:2021年福建省福州市初中毕业质量检测(二检)数学试题
10 . 点
,
,
在抛物线
上,其中
,
.点D在第四象限,直线
交x轴于点M,且
.
(1)若
,
①求该抛物线的解析式;
②
是该抛物线上的动点,连接
交y轴于点N,点Q的坐标为(0,4),求
面积的取值范围;
(2)连接
,点K在线段
上,
,
.将抛物线
平移,若平移后抛物线的顶点仍在原抛物线上,判断平移后的抛物线是否经过点K,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650de2e162669f2a6599240882260566.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2ff8b32c4dbfdf5d9e604ee77ad48e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87e5ea2efcb5a7daceabb4867f5e97c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc090563b7c08fd667cb16078bc3ddb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29df306e6ce3772b2246fc96101f985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e40d042b2b25c61ec3972e8202725321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35333abd7f02d663d15251bc5cbbf921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc13fe21e64d9b45614ed43be847904.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2f7174773db8f876f5074867c195757.png)
①求该抛物线的解析式;
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f79dd5014a28faeb0f18d5a7758b30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e43acfc591c6493bb06de927aeffd.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e7facb932529ae0d511d77714cf9e73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e138ccb316ed5ca1cf2c8e0525a6d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc090563b7c08fd667cb16078bc3ddb.png)
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