名校
1 . 已知:如图,
平分
,
,
交
的延长线于点
,且
.求证:
是等边三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/247b838f89222eb2b270817b95b95f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc59641467014c8be833e0781f04b1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb49df05f2e31d005735c3f14a21d30.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/24/03c77745-27d3-48ce-b94f-9bc47a191639.png?resizew=166)
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2023-11-19更新
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67次组卷
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2卷引用:河南省新乡市红旗区新乡市第一中学2023-2024学年八年级上学期期中数学试题
2 . 下列三角形:①有两个角等于
的三角形;②有一个角等于
的等腰三角形;③三个外角(每个顶点处各取一个外角)都相等的三角形;④一腰上的中线也是这条腰上的高的等腰三角形,其中是等边三角形的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ad1b0a76a887783392268ae203ad22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ad1b0a76a887783392268ae203ad22.png)
A.1个 | B.2个 | C.3个 | D.4个 |
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3 . 下列命题是假命题的是( )
A.有一个角为![]() |
B.三角形三条角平分线交于一点,并且这一点到三条边的距离相等 |
C.钝角三角形一定有一个角大于![]() |
D.同位角相等 |
您最近一年使用:0次
4 . 有下列命题:①对顶角相等;②两点之间,直线最短;③有一个角是
的三角形是等边三角形;④三角形外角和为
.其中真命题有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe639eab78eafd2d40ea70aa5d3f21d.png)
A.1个 | B.2个 | C.3个 | D.4个 |
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5 . 如图,
,
分别为
轴,
轴的正半轴上的点,作
关于坐标轴的对称线段
和
.
(1)如图(1),若
,
,直接写出点
,
的坐标;
(2)如图,
是
上一点,直线
交
于点
,
.
①如图(2),求证:
;
②如图(3),
平分
交
于点
,交
于点
,若四边形
的面积等于
面积的一半,判断
的形状,并证明你的结论.
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/12/677016df-c3c2-4dde-8759-e55b0da4c87b.png?resizew=400)
(1)如图(1),若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/434845564fd5765244f8d1aa9240fa39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e03f416cb4d50a5f473df4bbceeb3094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d96a5d40d0aea9f4398ca4d0fe9b0dd.png)
①如图(2),求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d37325793e54751bf28f15384606688d.png)
②如图(3),
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6655e2fa64a32cd12fe0279afd65d73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f24a8190430bd48d182c911506e74da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fb6e81fee5674c3e26a65e58cc506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2023-11-08更新
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163次组卷
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2卷引用:湖北省武汉市江汉区2023-2024学年八年级上学期期中数学试题
6 . 如图①,在一张长方形纸片
上画一条线段
,将纸片沿线段
折叠(如图②),当
时,试问重叠部分的
是什么三角形,请说明理由(注:长方形纸片对边平行,即:
)\
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa29fe6cd9eb51c184f6299d437375cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa29fe6cd9eb51c184f6299d437375cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ee4e0de0c1de0835766b7f627f348c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2e4f9a9fd59ac8fde1cd5e456003e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d474b8cf554bed0cafd7db7f7c0a9e42.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/21/0a484b26-1df9-4074-b64d-9c72daa1ad0a.png?resizew=350)
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名校
7 . 如图,在
中,点P为
边上一点.
(1)尺规作图:请在
上求作一点D,使得
(保留作图痕迹,不写作法).
(2)在(1)的条件下,
,
,求证:
是等边三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/12/0e9c900d-7bff-497e-bc33-63656b13a4e4.jpg?resizew=120)
(1)尺规作图:请在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216e4003cb76fc52b251e38a0afdd202.png)
(2)在(1)的条件下,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b8b98b2f83279a49e94d9f48c5e6f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7fbd6b9f85c086ac95562fe45e8d969.png)
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2023-11-07更新
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3卷引用:福建省福州第一中学2023-2024学年八年级上学期期中数学试题
8 . 若
,
,请添加一个条件使
是等边三角形______ .(写出一个即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/872b8b280a0ea1979d26c83b292b69e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
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7卷引用:福建省三明市尤溪县2022-2023学年八年级下学期期中数学试题
福建省三明市尤溪县2022-2023学年八年级下学期期中数学试题(已下线)第04讲 等腰三角形的判定定理(10类题型)-【帮课堂】2023-2024学年八年级数学上册同步学与练(浙教版)(已下线)北京市海淀区2023-2024学年八年级上学期期中模拟数学试题B卷吉林省松原市前郭县北片名校调研2023-2024学年八年级上学期期中数学试题山东省临沂市兰山区2023-2024学年八年级上学期期中数学试题安徽省淮南市西部地区2023-2024学年八年级上学期期末数学试题江西省南昌市青山湖区2023-2024学年下学期八年级期中数学试题
9 . 如图,
,
,
,求证:
是等边三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b4908b37cf23de34d38ae7a0bff278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f11e9afb1c3b15f364f2c95ca3a41d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9685ab781f942a3e28b2f39778515185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfa1a2af7e38d33634c462300df381f.png)
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3卷引用:吉林省长春市力旺实验初级中学2023-2024学年八年级上学期第一次月考数学试题
名校
10 . 问题情境:在数学实践课上,老师让小组合作探究两个完全相同的含
角的三角板拼图间存在的关系.
如图,
,
,
,
.
操作探究:
(1)如图①,当D、C、B在同一条直线上时,判断直线
与直线
的位置关系并证明;
(2)如图②,将图①中的三角板
绕点C顺时针旋转
,边
与边
交于点G,判断此时
的形状并证明;
(3)如图③,将图①中的三角板
绕点C顺时针旋转,边
与边
交于点M,当
是以
为腰的等腰三角形时,直接写出
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dff09ef655b39f25d7c7553c9dcc5d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc75953bf5dcfa4af308c34bf9952d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45fbc42ea04e6ae3b868f218785c9bed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9261cb9e2b240e14c11105289911a1ed.png)
操作探究:
(1)如图①,当D、C、B在同一条直线上时,判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
(2)如图②,将图①中的三角板
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678b28fddb166d90878d24d6e5481080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcaecf08a22124a457128fb04c9c02bb.png)
(3)如图③,将图①中的三角板
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678b28fddb166d90878d24d6e5481080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8045b729b7f257861057191a8a2388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
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2卷引用:吉林省四平市铁东区第三中学校2023-2024学年九年级上学期期中数学试题