1 . 两个直角三角形全等的条件是( )
A.一对锐角对应相等 | B.一对边对应相等 |
C.两直角边对应相等 | D.两个角对应相等 |
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2 . 阅读下面材料,完成相应任务:
尺规作图
尺规作图是指用无刻度的直尺和圆规进行作图.无刻度的直尺不具有度量长度的功能,它用来作经过两点的直线,射线或线段.圆规用来画弧,圆规的两脚还可以截取线段或两点之间的长度.尺规作图的关键是确定线与线,线与弧,弧与弧的交点,从而构造出符合要求的图形.
在数学课上,在用尺规作角的平分线时,同学们自主探究出很多不同于教材的作法.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/ab291480-6c0a-449e-b6f8-1cafcb032555.png?resizew=143)
已知:
求作:
的平分线.
小明的作法:如图①,在射线
上取点
,分别以
为圆心,
长为半径画弧,交射线
于点
,连接
交于点
,过点
画射线
,则射线
为
的平分线.
小华的思路:如图②,在
上任取一点
,在
的右侧作射线
,使得
,在射线
上取一点
,使
,过点
画射线
,则射线
是
的平分线.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/2cc60164-fdf8-46eb-9cf6-42fed9058a3e.png?resizew=301)
赵老师因势利导,引导同学们对各种作法进行研究,在感受教材作法简洁的同时体会它们的共同之处,即基于角的轴对称性构造全等三角形,得出两个相等的角.
任务一:小明的作法中,可以得出
,请你写出这一结论所依据的数学定理或基本事实.
任务二:根据小华的思路完成下列问题:
(1)使用直尺和圆规,在图②中补全图形(保留作图痕迹);
(2)根据小华的作法,证明
是
的平分线.
尺规作图
尺规作图是指用无刻度的直尺和圆规进行作图.无刻度的直尺不具有度量长度的功能,它用来作经过两点的直线,射线或线段.圆规用来画弧,圆规的两脚还可以截取线段或两点之间的长度.尺规作图的关键是确定线与线,线与弧,弧与弧的交点,从而构造出符合要求的图形.
在数学课上,在用尺规作角的平分线时,同学们自主探究出很多不同于教材的作法.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/ab291480-6c0a-449e-b6f8-1cafcb032555.png?resizew=143)
已知:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
小明的作法:如图①,在射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecdba36d4c2d4acedbd44d08e4c04127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da58a347512f4fc726cba055312c00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec38bedb55b02c42c1fb552e6cbf7a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5557e3f084429321ddea623574d26e17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
小华的思路:如图②,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667db777bce5dc053916871fce18ec9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e795d041c170e2a62ff1157becd7f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/2cc60164-fdf8-46eb-9cf6-42fed9058a3e.png?resizew=301)
赵老师因势利导,引导同学们对各种作法进行研究,在感受教材作法简洁的同时体会它们的共同之处,即基于角的轴对称性构造全等三角形,得出两个相等的角.
任务一:小明的作法中,可以得出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e675ce3a46689f8f49c18059ed537503.png)
任务二:根据小华的思路完成下列问题:
(1)使用直尺和圆规,在图②中补全图形(保留作图痕迹);
(2)根据小华的作法,证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
您最近一年使用:0次
名校
3 . 下列命题正确的是( )
A.两边及一角对应相等的两个三角形全等 |
B.将32000精确到千位,记为![]() |
C.16的平方根是4 |
D.到三角形三个顶点距离相等的点在这个三角形三边的垂直平分线上 |
您最近一年使用:0次
4 . 如图,在
中,
,
,
,
、
交于点
.在不添加字母和辅助线的情况下,请你在图中找出一对全等三角形并证明.
![](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/e2d212c1709b8e72a055cf1b5381ef64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02fbbe04651b37e1520bb9a7bafed509.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/4dd56200-a7c0-4472-b6b7-c03b75825f15.jpg?resizew=136)
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5 . 如图,已知
,以点O为圆心,任意长为半径画弧,分别交
,
于点C,D;再以点O为圆心,大于
为半径画弧,分别交
,
于点E,F;连接
,
,则
,其全等的依据是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/47278fdc-330d-4313-9e84-7d28a5fb9c04.png?resizew=122)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.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/828628c0876b45381c9a0edeb0fec236.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/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4901df744267fa7c163f254206a7202.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/47278fdc-330d-4313-9e84-7d28a5fb9c04.png?resizew=122)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 如图,若
,
,
,则
的依据是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/24/baf8b41c-9af0-4300-a060-b791ea0bf6a8.png?resizew=124)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a510a3eb906b3ef0760b0d1723d11ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c244edbf77fbb8e9c017515e370c5c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439fbb8974a5f907205d26b47b420bf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ca10806fc8c3c3efd6859f526b76900.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/24/baf8b41c-9af0-4300-a060-b791ea0bf6a8.png?resizew=124)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
7 . 已知:如图,
,点C,点F在
上,
,
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd81adb13f5a7550b0f94f770900a613.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7f27111303c38eaf43bf547e460a33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a510a3eb906b3ef0760b0d1723d11ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac61f3477e623aa4f924a82bd7a06ce4.png)
![](https://img.xkw.com/dksih/QBM/2023/11/9/3363995858313216/3420746288701440/STEM/b9851282b1e743769f1977960481f353.png?resizew=187)
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2024-01-28更新
|
73次组卷
|
14卷引用:浙江省温州市第二十一中学2020-2021学年八年级上学期第一次阶段测试数学试题
浙江省温州市第二十一中学2020-2021学年八年级上学期第一次阶段测试数学试题广东省广州市越秀区广东实验中学越秀学校2020-2021学年八年级上学期期中数学试题湖北省黄冈市浠水县兰溪镇兰溪初级中学2022-2023学年八年级上学期11月期中考试数学试题广东省雷州市第八中学2022-2023学年八年级上学期数学期中测试题广东省广州市天河区广东实验中学附属天河学校2020-2021学年八年级上学期期中数学试题广东省中山市秋纪念中学2021—2022学年八年级上学期期中联考数学试题湖北省黄冈市浠水县兰溪中学2022-2023学年八年级上学期期中数学试题广东省江门市台山市育英中学2023-2024学年八年级上学期期中数学试题新疆维吾尔自治区和田地区墨玉县2023-2024学年八年级上学期期中数学试题新疆克孜勒苏柯尔克孜自治州阿克陶县梧桐中学2023-2024学年八年级上学期数学月考测试题2019年福建省厦门第一中学九年级下学期第二次质量检测数学试题山东省菏泽市菏泽经济技术开发区多校联考2022-2023学年七年级下学期段考数学试题山东省菏泽市经开区多校联考2022-2023学年七年级下学期6月月考数学试题福建省厦门市集美实验学校2022-2023学年九年级下学期第一次月考数学试题
8 . 如图,点E,F在
上,
,
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/decd02bb1fd6ac5a3610a279fe96212b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de966c316db1013defc56372fcf814e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d4a94e65672e52bac3e6c927b0a66d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba06c3ea41c13a3cb01e46ffb0a4aee8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/21/7593b758-e044-4edd-ae71-1909ba8ae25a.png?resizew=140)
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9 . 如图,
,
,
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5b4ea605cf0b98e428d071f6be6762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6307019d82d2a2a51e0ffd4ebf345.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be5fc6ead6416492c231c320a5486f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa3115a985b37d25d325836409c7766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5007e72f2706deb1b843fa8e900279e6.png)
![](https://img.xkw.com/dksih/QBM/2024/1/22/3416849008549888/3418872045568000/STEM/e91113490c4a4685919f0291ef629b0c.png?resizew=149)
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10 . 如图,
,
,
,点
在线段
上以
的速度由点A向点
运动,同时,点
在线段
上以
的速度由点
向点
运动,它们运动的时间为
.当
与
全等时,
的值是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/6/7603c6b0-b6bb-432c-82cc-7bce9138ca5e.png?resizew=186)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cee49e97546d466ba3ee630e08cdc3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f6b2dcfd1fe3e7de1f11a3f08810337.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a014b0039fbe99fa8751a62521c28058.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d989a128e30a701dfff5592476a76bab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eac4bf88ef98138fca298444568d947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d744165d6aad705f64de41a9d931750a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147de24f071e316b68fd2e78e3c84545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8dcc9f79fe5f07f25447aa442ee14ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/6/7603c6b0-b6bb-432c-82cc-7bce9138ca5e.png?resizew=186)
A.2 | B.1或1.5 | C.2或3 | D.1或2 |
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