1 . 【阅读材料,拓展知识】
阅读下列材料:某校“数学社团”活动中,研究发现常用的分解因式的方法有提取公因式法、公式法,但还有很多多项式只用上述方法无法分解,如:“
,细心观察这个式子就会发现,前两项可以提取公因式,后两项也可提取公因式,前后两部分分别分解因式后产生了新的公因式,然后再提取公因式就可以完成整个式子的因式分解了,过程为
.
“社团”将此种因式分解的方法叫做“分组分解法”.
【应用知识,解决问题】
(1)因式分解:
;
(2)已知
,
,求
的值;
【提炼思想,拓展应用】
(3)
的三边
,
,
满足
,判断
的形状并说明理由.
阅读下列材料:某校“数学社团”活动中,研究发现常用的分解因式的方法有提取公因式法、公式法,但还有很多多项式只用上述方法无法分解,如:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1786b408b6152e0ee429327d5e944f26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c188f3d7d2a24c99ef654742c1b58198.png)
“社团”将此种因式分解的方法叫做“分组分解法”.
【应用知识,解决问题】
(1)因式分解:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad738bf5c87fe2bf1b632312fd90654d.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1734333c64d445ffb88d719827a1969c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c0e4e32994c092dacdde5842b7d0497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2cf1dc5de75d675cff8dac4fc03098a.png)
【提炼思想,拓展应用】
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab1348a38027a7329325c68cf34fbc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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名校
2 . 如图,在
中,
,
是斜边
的垂直平分线,分别交
、
于
、
两点,若
,则
的长是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26fdd8e57562ba94e10e7f1d770826d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eb3d1070981fed5ca65a34bb2282e6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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3 . 如图,在
中,
,
的垂直平分线交
于点E,垂足为D,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d3c9ce32b721995f355eea411340e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b753dbb5a670dd4f5e23bb919e44dda2.png)
A.30度 | B.60度 | C.36度 | D.40度 |
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4 . 如图,在由边长为1个单位长度的小正方形组成的网格中,
的顶点均为格点(网格线的交点).
向右平移4个单位长度,再向下平移2个单位长度,得到线段
,画出线段
;
(2)以点
为旋转中心,将
按逆时针方向旋转
,得到
,请画出
;
(3)在线段
上描出点
,使得
为
的角平分线.(作图过程用虚线表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/e6e490f703eb6c9bb1278c78ebc2d661.png)
(2)以点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
(3)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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3卷引用:2024年宁夏银川市景博学校九年级中考一模数学试题
5 . 如图,在
中,按照如下尺规作图的步骤进行操作:
交于M,N两点;
②分别以M,N为圆心,以适当长为半径画弧,两弧交于点D,作射线
与
交于点E;
③分别以B,C为圆心,以大于
的长为半径画弧,两弧交于点P,Q,作线段
与
于点F;
④连接
.
若
,
,则
的周长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4515e1dff9a852b3294dc1d6488a5748.png)
②分别以M,N为圆心,以适当长为半径画弧,两弧交于点D,作射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/761dd5f55ed3434fe1dfa6339a55e832.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
③分别以B,C为圆心,以大于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d452f74791f58e8400cb8d2d6038dc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3c3fd476a7ba1a5f746084513840f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
④连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2e02f64e9ffe7b0ea50805fa5e08cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff39c7aa648afd1080206c8080ff79e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5卷引用:2024年宁夏回族自治区 银川市 兴庆区银川市第十七中学二模检测数学试题
6 . 如图,将菱形
折叠,使点
落在
边的点F处,折痕为
.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e962382788c6e211bdf42a7a0fe45ef.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab642bee3d5db147a12df2cac5f5fbd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e962382788c6e211bdf42a7a0fe45ef.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/ead8f026-acf9-4898-9b22-da53791ba23c.png?resizew=186)
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2卷引用:2024年宁夏银川市兴庆区中考数学一模模拟预测题
7 . 如图,方格纸中的每个小方格都是边长为1个单位的正方形.
,点
在方格纸上的格点上,
;
(2)画出等腰三角形
,点
在方格纸上的格点上,
的面积为6,连接
,直接写出
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1070d38d2fea1dc88c6eb31d320b763.png)
(2)画出等腰三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14eec658f69c267a70c1e8f9b744e282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df7626240940eb340420a605e95aeee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
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2卷引用:宁夏回族自治区银川市兴庆区第十五中学2023-2024学年九年级下学期期中数学试题
8 . 如图,
中,
,
,
的中垂线
交
于
,交
于
,下述结论:(1)
平分
;(2)
;(3)
的周长等于
;(4)
是
中点.其中正确的命题序号是________ .
![](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/ee54b9b398ce80cd054b56173fe810f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.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/2a30f3a8b673cc28bd90c50cf1a35281.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/d9f520e0bec1a707da5101603e5210ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a9ec45721f7b4d1c99917ac0d970f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6151fb896230f2579d516af4c67e634a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/a6849f7f-66d6-4931-928c-03b235f8ff96.png?resizew=129)
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9 . 如图,在
中,
,
的垂直平分线
交
于点C,连接
,若
,那么
的度数是________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b32e5f08d3d4dbadcfce8cc894f60f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.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/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febc9a89d0d1c97b88c0f4acd32b4e67.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/e71934cb-67c8-47fe-bd6b-f1dd07f3e058.png?resizew=224)
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10 . 等腰三角形的一个角是
,则它的另外两个角的度数分别是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27ef3e89c37d21fd86537bee7c57b053.png)
A.![]() ![]() | B.![]() ![]() | C.![]() ![]() | D.![]() ![]() |
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2024-02-05更新
|
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2卷引用:宁夏回族自治区吴忠市盐池县2023-2024学年八年级上学期期末数学试题