1 . 综合与实践
如图,
是
的切线,
为切点,
是圆上与
不重合的两点.
(1)如图1,若
是
直径,
,则
________.
问题探究
(2)如图2,当
为
上任意一点时,
与
有怎样的关系?并加以证明.
拓展运用
(3)如图3,
的半径是2,
,求
的大小.
如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0520e9675bc1b416e8b8f01eb69fd13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)如图1,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed09914814b6abbfb04769ca7ca24567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc79fee8f7996b58dbed724fe6afcddb.png)
问题探究
(2)如图2,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c32986401a4d24904d5e446fa9210ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febc9a89d0d1c97b88c0f4acd32b4e67.png)
拓展运用
(3)如图3,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b968d9de81b3730d6b2bb9dba8ed0de4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
您最近一年使用:0次
2024-04-03更新
|
66次组卷
|
2卷引用:贵州省遵义市新蒲新区2023年初中生毕业认定测试九年级数学模拟预测题
2 . 探究式学习是新课程倡导的重要学习方式,某兴趣小组拟做以下探究.
在
中,
,
,D是
边上一点,且
(n为正整数),E是
边上的动点,过点D作
的垂线交直线
于点F.
【初步感知】
(1)如图1,当
时,兴趣小组探究得出结论:
,请写出证明过程.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/a57186cb-bf01-45c1-a8e5-dfce5ba356bb.png?resizew=197)
【深入探究】
(2)如图2,当
,且点F在线段
上时,试探究线段
之间的数量关系,请写出结论并证明.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/d06f3aba-0df2-4bb4-ace0-0b4179366fdd.png?resizew=191)
【拓展运用】
(3)请通过类比、归纳、猜想,探究出线段
之间数量关系的一般结论(直接写出结论,不必证明).
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825671c551cc4593793b40c43d46757a.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
【初步感知】
(1)如图1,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36978e392c8df4668ed3f74641febbfe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/a57186cb-bf01-45c1-a8e5-dfce5ba356bb.png?resizew=197)
【深入探究】
(2)如图2,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30bf3421adec0637c315309c2ea9a24.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/d06f3aba-0df2-4bb4-ace0-0b4179366fdd.png?resizew=191)
【拓展运用】
(3)请通过类比、归纳、猜想,探究出线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30bf3421adec0637c315309c2ea9a24.png)
您最近一年使用:0次
名校
3 . 【问题发现】
(1)如图1所示,
和
均为正三角形,B、D、E三点共线.猜想线段
,
之间的数量关系为 ;
;
【类比探究】
(2)如图2所示,
和
均为等腰直角三角形,
,
,
,B、D、E三点共线,线段
、
交于点F.此时,线段
,
之间的数量关系是什么?请写出证明过程并求出
的度数;
【拓展延伸】
(3)如图3所示,在
中,
,
,
,
为
的中位线,将
绕点A顺时针方向旋转,当
所在直线经过点B时,请直接写出
的长.
(1)如图1所示,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8cfb5b3f527ff16771f6cb4741f19bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83873a9d782f2588c5eedbfe73f9bc2f.png)
【类比探究】
(2)如图2所示,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd9776aa108071b50b71adf181bbdaf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d00572a90232e08932317af2a53767.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.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/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6282292819434a8905a212427613fd85.png)
【拓展延伸】
(3)如图3所示,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d3c9ce32b721995f355eea411340e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07140f277a35733d8c97577ccdd4e3ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
您最近一年使用:0次
2024-03-24更新
|
495次组卷
|
19卷引用:2023年贵州省遵义市第十二中学九年级下学期第一次模拟数学试题
2023年贵州省遵义市第十二中学九年级下学期第一次模拟数学试题2023年山东省济南市历城区中考二模数学试题2023年山东省泰安市泰山博文中学二模数学试题2023年广东省广州市白云区华赋学校中考二模数学试题2023年山东省济南市章丘区博雅新世纪实验学校中考三模数学试题2024年山东省青岛市中考数学一模模拟试题2023年山东省济南市章丘区新世纪博雅实验学校中考数学三模模拟试题2024年河南省中考数学复习模拟试题(九)2024年广西中考数学一模模拟预测题山东省济南市历下区2022-2023学年九年级上学期期末数学试题广东省深圳市龙岗区翠枫学校2022-2023学年八年级下学期期中数学试题广东省深圳市龙岗区塘坑学校2022-2023学年八年级下学期期中数学试题(已下线)2023年广州等市二模(几何综合)(已下线)2023年济南二模(几何综合)河北省石家庄市2023-2024学年九年级上学期期末模拟数学试题山东省青岛市市南区2023-2024学年九年级上学期期末数学试题河南省驻马店市新蔡县2023-2024学年九年级上学期期末数学试题山东省济南市历下区2022-2023学年九年级上学期期末数学试题(已下线)2024年四川省成都市中考数学真题变式题24-26题
4 . 在中,
,
是直角三角形,
,
点
是
的中点.
【初步发现】
如图①,当的顶点
在边
上时,若
,猜想
与
的数量关系,并写出(不需要证明);
【猜想验证】
小红说:在【初步发现】的条件下,还可得到线段.你认为她的说法正确吗?说明理由;
【拓展延伸】
如图②,当的顶点
在边
上时,若
,探究线段
与线段
的数量关系,并说明理由.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/22/b728ecff-dfd7-4b61-a2e0-01525d06a94f.png?resizew=392)
您最近一年使用:0次
2024·贵州·一模
5 . 如图,在等腰三角形
中,
,以
为直径的
与
交于点
,
,垂足为
,
的延长线与
的延长线交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/23/7c850fc9-66ef-4ef1-8486-9a6d7dbf074d.png?resizew=169)
(1)求证:
是
的切线;
(2)若
的半径为5,
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.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/68fbbd17c89f03dbb61cd6ffdb9a0344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/23/7c850fc9-66ef-4ef1-8486-9a6d7dbf074d.png?resizew=169)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eb3d1070981fed5ca65a34bb2282e6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
您最近一年使用:0次
6 . 如图甲,正方形
和等腰直角
有公共点
,点
是直线
上一动点,连接
,取
的中点
,连接
.
(1)【方法体会】线段
,
有着特别的关系,请依据思路将横线处补充完整.
解:在图甲中,将线段
延长至点
,使
,连接
,
,交
于点
.
则:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a1e0c08b99addcc37e4176f5882e8f.png)
即:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9195d58eb86b8cfacc37f3782eec27a7.png)
在
和
中:
∵![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c20968b91619283dd0bf4810cd3086.png)
∴______(
)
∴
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81f683bfa5fb4f5d901503bfa7ccf26.png)
设
,
交于点
,
又∵![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e655be1d2908b97ed4df568a10177013.png)
∴![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6d4df1654d5d59864a7d4fd3bd27dd.png)
∴
,即![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79216c6a32bb699aeb36144da020490.png)
又∵点
是
中点,点
是
中点
∴
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14985aca12e83ce0d6400b65857c9a0.png)
又∵
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79216c6a32bb699aeb36144da020490.png)
∴
,
的位置关系是
_____;数量关系是______.
(2)【探索发现】如图乙,
交
于点
,交
于点
,交
于点
,当点
与点
重合时,求
:
的值;
(3)【拓展运用】若正方形的边长为
,连接
,
,在点
运动的过程中,当
时,请在备用图中画出此时的图形,并求出此时
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/862730f28c12750ebea0af5edcac5fef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef9d0784478511736255074b9395fae.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/22/5a5fa1b3-5fba-4355-8120-99cda6f5fdce.png?resizew=509)
(1)【方法体会】线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef9d0784478511736255074b9395fae.png)
解:在图甲中,将线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faee0268e5ede6318697e5a8509dd6f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90c579436ff500a36fe7976012bc227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc8b62dc033d86ee9e561b8903796701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb11667abcb2759f301391b9850352be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
则:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a1e0c08b99addcc37e4176f5882e8f.png)
即:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9195d58eb86b8cfacc37f3782eec27a7.png)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcaecf08a22124a457128fb04c9c02bb.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c20968b91619283dd0bf4810cd3086.png)
∴______(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d7d84e698f6d38fa2be14d36c04988.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/343f75b2c5479c279abca2faed278901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81f683bfa5fb4f5d901503bfa7ccf26.png)
设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cdd9f345915ae742ed3dcd3f9678264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/22/06ea4ec9-979b-4a8e-b791-ecdd1567f6b0.png?resizew=236)
又∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e655be1d2908b97ed4df568a10177013.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6d4df1654d5d59864a7d4fd3bd27dd.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86129aef281bd7f5da10963e5164d6b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79216c6a32bb699aeb36144da020490.png)
又∵点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87448e09eaa816e50ae92d111d5ded6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8120f2eeb724c756b5f84a14c6df527.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe5747aaac225fd08ad9789789b3804.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14985aca12e83ce0d6400b65857c9a0.png)
又∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/343f75b2c5479c279abca2faed278901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79216c6a32bb699aeb36144da020490.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef9d0784478511736255074b9395fae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bff235ce9338aeef7f2b952079cbb0f.png)
(2)【探索发现】如图乙,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef9d0784478511736255074b9395fae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/f0a36775168095280f72504478345bce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f37d57768f163f56619e531b9541ab.png)
(3)【拓展运用】若正方形的边长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1165830b314a0dab65ea267e82bd3f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f30cb81835298cb612a828f355060a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd63ce2206748eb84eb2bebf459e754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e323c08b18488d11bd8f3cd74efa971a.png)
您最近一年使用:0次
2024-03-22更新
|
106次组卷
|
2卷引用:2024年贵州省部分学校2024年初中一模试题
7 . 已知在正方形
中,
,点E,F分别在边
,
上,且
,连接
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/24/b94d1ab9-2cff-4ac7-a290-4836e2b7372b.png?resizew=289)
(1)如图1,连接
交
于点G,若
,求证:
;
(2)如图2,连接
,
,若
,求
的长;
(3)如图3,连接
,过点E作
,垂足为M,交
于点N,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7faabc484ce3666706c1beffda4bcfe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0213c5787a5a6b38d11bceca5567f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/24/b94d1ab9-2cff-4ac7-a290-4836e2b7372b.png?resizew=289)
(1)如图1,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ff575e55857af133edb24c8e61504f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/330a1dbd5b7700f821750fc8192ec9bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/429dab5e1dc3ec23c08718609fb9237c.png)
(2)如图2,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c4eccda4edcee29a5f15609e85106df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a974e7873a7addd612e5abd107f7a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
(3)如图3,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c4eccda4edcee29a5f15609e85106df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b87516d02001590a14b4df66bbd469c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d64bab81a5dfca87b1770519630fb1b.png)
您最近一年使用:0次
2024-03-22更新
|
155次组卷
|
4卷引用:2024年贵州省部分学校大联考中考一模数学模拟试题
2024年贵州省部分学校大联考中考一模数学模拟试题2024年安徽省芜湖市鸠江区部分学校中考一模数学试题安徽省淮北五校联考2023-2024学年九年级下学期月考数学试题(已下线)热点05 三角形(10大题型+满分技巧+限时分层检测)-2024年中考数学【热点·重点·难点】专练(广东专用)
8 . 四边形ABCD内接于
,
.
,求
的度数;
(2)如图2.连接
交
于点E.
①求证:
;
②若
,
,
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb2cf0e95fdf1fd8a5b01d3dfd905e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3981e7286d41960daf4e110c1c84e03a.png)
(2)如图2.连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49bbeec98d7c80322952068ae4786781.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1481cad5968b766f7b309541ed1b252.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
2024-03-22更新
|
373次组卷
|
6卷引用:2024年贵州省部分学校大联考中考一模数学模拟试题
2024年贵州省部分学校大联考中考一模数学模拟试题2024年安徽省芜湖市鸠江区部分学校中考一模数学试题安徽省淮北五校联考2023-2024学年九年级下学期月考数学试题(已下线)重难点05数形结合思想在三类题型中的应用-2024年中考数学【热点·重点·难点】专练(安徽专版)(已下线)专题07 与圆有关的证明与计算问题-2024年中考数学二轮热点题型归纳与变式演练(江苏专用)(已下线)抢分秘籍10 圆中证切线、求弧长、求面积、新定义探究问题(压轴通关8题型)-备战2024年中考数学抢分秘籍(全国通用)
9 . 如图,在
中,
,
于点
.
;
(2)若
,
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2e57024080bfa448510135535fd7887.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714cc3707bba3bfdb56e251999be8592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
2024-03-22更新
|
148次组卷
|
3卷引用:2024年贵州省部分学校大联考中考一模数学模拟试题
10 . 如图,在矩形
中,
,点E,F分别在
上,且
,连接
,
,连接
交
于点M,交
于点N,则下列结论中错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c4e4a162f12d12a082b8d8fdd1aeab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e545f31f7cc57a31843f5adfd02941.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee498e34b21dea01638f5c6adccb3561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de7cb98ebad4ce465a7c02fc1c3b5e0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d1c709cbc7baefbc4f22b57991a991.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-03-22更新
|
158次组卷
|
5卷引用:2024年贵州省部分学校大联考中考一模数学模拟试题
2024年贵州省部分学校大联考中考一模数学模拟试题2024年安徽省芜湖市鸠江区部分学校中考一模数学试题安徽省淮北五校联考2023-2024学年九年级下学期月考数学试题(已下线)专题05 四边形(6大易错点分析)-备战2024年中考数学考试易错题(安徽专用)(已下线)热点05 三角形(10大题型+满分技巧+限时分层检测)-2024年中考数学【热点·重点·难点】专练(广东专用)