1 . 若△ABC的三边长分别为a,b,c.下列条件:①∠A=∠B﹣∠C;②a2=(b+c)(b﹣c);③∠A:∠B:∠C=3:4:5;④a:b:c=5:12:13.其中能判断△ABC是直角三角形的是_____ (填序号).
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5卷引用:内蒙古呼和浩特市回民区2020-2021学年七年级下学期期中考试数学试题
名校
2 . 如图,
,
的平分线交
于点
,
是
上的一点,
的平分线交
于点
,且
,下列结论:
①
平分
;
②
;
③与
互余的角有2个;
④若
,则
.
其中正确的是______________ .(请把正确结论的序号都填上)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d527b7de54224cc1698843a59a19a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752fa646a2d9cfca34001748445301c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a14654f44613e7dc85413f173e5cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4d5ff57f147aa0628fdd47899b5a132.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af342d3b871ace448ccc7c648528288.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df5466383bedd9dd915a8788547d730.png)
③与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685516a27697104e83b311d76efa17aa.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd465973943bcd766b5275ee204bbf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdd38d3ae52434be8c63e1ad458b09d0.png)
其中正确的是
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4卷引用: 山东省滨州市滨城区2021-2022学年七年级下学期期中考试数学试题
3 . 已知
中,
,
,现有以下这些条件:①
;②
;③
;④
.要使
的形状和大小都是确定的,可以添加的条件是______
(写出所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735bd70c2fa2bf51fd7aa448b20d0be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3018c687427b6257767eda4a8c6612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f89deb952f57f4b3fa4887b098b7b91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9ba2098ed6b4137b08932524b72ba37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5fe8897de9cd1844303353867e945f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
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2卷引用:福建省福州市马尾区琅岐中学2021-2022学年八年级上学期期末数学试卷
21-22八年级上·浙江杭州·期末
4 . 如图,在△ABC中,∠ACB=90°,D为AB上任一点,过D作AB的垂线,分别交边AC、BC的延长线于E、F两点,∠BAC、∠BFD的平分线交于点I,AI交DF于点M,FI交AC于点N,连接BI.下列结论:①∠BAC=∠BFD;②∠ABI=∠FBI;③AI⊥FI;④∠ENI=∠EMI;其中正确结论的序号是_________ .
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/8/bdc430b7-0dd0-4123-b600-bf92f6a2aa8a.png?resizew=138)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/8/bdc430b7-0dd0-4123-b600-bf92f6a2aa8a.png?resizew=138)
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5 . 如图,已知AC平分∠BAD,CE⊥AD于点E,BC=CD.有下列结论:①∠ABC+∠ADC=180°;②AB+AD=2AE;③∠CBD=∠CAB;④AD﹣AB=2DE.其中正确结论的序号是 _______ .
![](https://img.xkw.com/dksih/QBM/2021/12/1/2862911525904384/2863088230195200/STEM/b5831089-0c98-4348-b84a-58ee2a70d7df.png?resizew=159)
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2卷引用:广东省广州市第二中学2021-2022学年八年级上学期期中数学试题
6 . 数学概念:如图①,在△ABC中,D为∠ABC的对边AC上一点(点D不与点A、C重合),连接BD.若∠ADB和∠CDB这两个角中至少存在1个与∠ABC相等,则称BD为△ABC中∠ABC的等角分割线.
![](https://img.xkw.com/dksih/QBM/2021/10/29/2839691527626752/2914084275544064/STEM/e658bece-a4a4-44ae-be2f-fcb31a9e1f89.png?resizew=268)
(1)概念理解:如图②,在Rt△ABC中,∠C=90°,∠B=60°.分别画出∠B和∠C的等角分割线BD、CE.(画图工具不限,并做出适当的标注)
(2)知识运用:在△ABC中,∠A=50°,∠ACB=70°.已知∠ABC、∠ACB的等角分割线BD、CE相交于点O,求∠BOC的度数.
(3)深入思考:下列关于“等角分割线”的结论:
①钝角三角形中的钝角有2条等角分割线;
②三个角都不相等的三角形中,最小的角没有等角分割线;
③三角形的高、角平分线可能是该三角形中的等角分割线;
④任意一个三角形中最少有1条等角分割线,最多有3条等角分割线.
其中所有正确结论的序号是 .
![](https://img.xkw.com/dksih/QBM/2021/10/29/2839691527626752/2914084275544064/STEM/e658bece-a4a4-44ae-be2f-fcb31a9e1f89.png?resizew=268)
(1)概念理解:如图②,在Rt△ABC中,∠C=90°,∠B=60°.分别画出∠B和∠C的等角分割线BD、CE.(画图工具不限,并做出适当的标注)
(2)知识运用:在△ABC中,∠A=50°,∠ACB=70°.已知∠ABC、∠ACB的等角分割线BD、CE相交于点O,求∠BOC的度数.
(3)深入思考:下列关于“等角分割线”的结论:
①钝角三角形中的钝角有2条等角分割线;
②三个角都不相等的三角形中,最小的角没有等角分割线;
③三角形的高、角平分线可能是该三角形中的等角分割线;
④任意一个三角形中最少有1条等角分割线,最多有3条等角分割线.
其中所有正确结论的序号是 .
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7 . 如图,已知AM∥BN,∠A=64°,点P是射线AM上一动点(与点A不重合),BC、BD分别平分∠ABP和∠PBN,分别交射线AM于点C、D,下列结论:
①∠ACB=∠CBN;②∠CBD=64°;③当∠ACB=∠ABD时,∠ABC=29°;④当点P运动时,∠APB:∠ADB=2:1的数量关系不变.其中正确结论的有_________ (填序号).
①∠ACB=∠CBN;②∠CBD=64°;③当∠ACB=∠ABD时,∠ABC=29°;④当点P运动时,∠APB:∠ADB=2:1的数量关系不变.其中正确结论的有
![](https://img.xkw.com/dksih/QBM/2021/7/7/2758895482748928/2796137544761344/STEM/7dc3fe69-93da-4b92-8369-09d765b19322.png)
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8 . 三角形中,如果一个角是另一个角的3倍,这样的三角形我们称之为“灵动三角形”.例如,三个内角分别为120°、40°、20°的三角形是“灵动三角形”.如图,∠MON=60°,在射线OM上找一点A,过点A作AB⊥OM交ON于点B,以A为端点作射线AD,交线段OB于点C(我们规定0°<∠OAC<90°).下列结论正确的是_____ .(填入正确序号)
①∠ABO的度数为30°;
②△AOB不是“灵动三角形”;
③若∠BAC=70°,则△AOC是“灵动三角形”;
④当△ABC为“灵动三角形”时,∠OAC为30°或52.5°.
①∠ABO的度数为30°;
②△AOB不是“灵动三角形”;
③若∠BAC=70°,则△AOC是“灵动三角形”;
④当△ABC为“灵动三角形”时,∠OAC为30°或52.5°.
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4卷引用:山东省济南育英中学2020-2021学年七年级下学期期中数学试题
9 . 如图,已知
,
、
为
上的两点,
、
为
上的两点,延长
于点
,
平分
,点
在直线
上,且
平分
,若
.则下列结论:①
;②
;③
;④设
,
;⑤
的度数为50°.其中正确结论为______ .(填序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29eddca555d1ee6f1c7061efbaf11b47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/040014a609bb4c2c2f16f223467e4871.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c707b3dd1280fb11855b8d33296a500.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1abefbb8569ee75778d9d8aae9128f47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/224efa375375f1ac848b0c15ee51aebd.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/6/cfd08173-3dfc-4c7f-b915-75a70cb09158.png?resizew=233)
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10 . 如图,直角三角形
中,
,
于点
,
平分
交
于点
,交
于点
,
交
于点
,
于
,以下4个结论:①
;②
是等边三角形;③
;④
中正确的是______ (将正确结论的序号填空)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21b28f28ced0531d1df34fcf04c6c67f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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![](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/fac4e5834821241bf9752e7986e0defa.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53bb5ccceb997622add983ee2dc68522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd6fe78f6cfdfefd6d8be45473b25b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff39c7aa648afd1080206c8080ff79e.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb29dc024f8f554eaa879bac345aeb92.png)
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6卷引用:山东省滨州市惠民县2020-2021学年八年级上学期期末数学试题
山东省滨州市惠民县2020-2021学年八年级上学期期末数学试题湖北省咸宁市2020-2021学年八年级下学期4月教学质量监测数学试题(已下线)专题4.6平行四边形【压轴题型专项训练】-2020-2021学年八年级数学下学期期末专项复习(北师大版)福建省龙岩市上杭县城区三校2021-2022学年八年级下学期期中检测数学试题天津市东丽区英华学校2022-2023学年八年级下学期第一次月考数学试卷广东省广州市海珠区南武集团2022--2023学年八年级下学期期中数学试题