1 . 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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/721c75fcd58d3d54260aad0f82e09e37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e99c17d72c203b50802f19d4731545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/040014a609bb4c2c2f16f223467e4871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3a92cc55943edb5d4d91b6b5729d7a8.png)
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0fc832cde7c7264f1692fb8d415eb66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9fe609f7851c20ad9a6892f080a0ff.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/6/cfd08173-3dfc-4c7f-b915-75a70cb09158.png?resizew=233)
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2 . 如图,锐角三角形
中,点D在
上,
.甲、乙二人想在
上找一点P,使得
,做法分别如下.对于甲、乙二人的做法,下列判断正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787ac5e13622afab5e9f8603afe42356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a2906712896678ab53d2e5df18535ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/078c13354d27e9ed4131792a8e43454c.png)
甲的做法![]() 作 ![]() ![]() | 乙的做法![]() 以点C为圆心, ![]() ![]() |
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/19/dd7c4d23-64a8-4fdb-b3b2-412878dfc9d2.png?resizew=134)
A.甲、乙皆正确 | B.甲、乙皆错误 | C.甲正确,乙错误 | D.甲错误,乙正确 |
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名校
3 . 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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4 . 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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2021-08-26更新
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283次组卷
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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
5 . 如图,在
中,
和
的平分线相交于点
,过点
作
交
于点
,交
于点
,过点
作
于点
,下列四个结论:
①
;②
;
③点
到
各边的距离相等;④设
,
,则
.
其中正确的结论是__________ .(填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/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39b12aa9d4f934868c3e4f51f73e7c89.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a11c1db76cc7e1894f74a50d71736455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f039772c881ab00f617c7cc90f9199.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ebe4c425939ccbf0ff723d8c2468da.png)
③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/b6470d85c2dc5ead1b7278ab602860e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc627ee5e84b139d4eaf3abb59f9a482.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70a2e2b1da286ae6321b2f41876ccc75.png)
其中正确的结论是
![](https://img.xkw.com/dksih/QBM/2020/3/26/2427724200263680/2428404448100352/STEM/6901c5781b434d15acce41c2eac045c6.png?resizew=152)
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2020-03-27更新
|
438次组卷
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5卷引用:【区级联考】广东省深圳市实验学校坂田校区2018-2019学年八年级上期期末测试数学试题
【区级联考】广东省深圳市实验学校坂田校区2018-2019学年八年级上期期末测试数学试题江苏省徐州市新沂市2019-2020学年八年级上学期期中数学试题(已下线)【新东方】 2020年1月江西南昌雷氏学校初二上学期期末数学试卷(已下线)专题冲刺小卷04 三角形-2020年《三步冲刺中考·数学》之最新模考分类冲刺小卷(广东专用)河南省郑州市金水区一八联合国际学校2020-2021学年八年级下学期期中数学试题
6 . 对于题目:“在
中,
,分别以A,B为圆心,以
长为半径的两条弧相交于点P,求
的度数”.嘉嘉求解的结果是
,淇淇说:“嘉嘉的解答正确但不全面,
还有另一个不同的值.”则下列判断中,正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59ae599c3e37765826272420b5eecb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac3c1375c64dceef45846308a418cf7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a25a30b945c0a306802a9d7748bccdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac3c1375c64dceef45846308a418cf7f.png)
A.淇淇说得对,![]() ![]() | B.淇淇说的不对,![]() ![]() |
C.嘉嘉求的结果不对,![]() ![]() | D.两人都不对,![]() |
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7 . 如图,
和
关于直线
对称,
和
关于直线
对称.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/24/8ad54631-6c59-4ef3-b5b4-f93b82942308.png?resizew=149)
(1)作出直线
(尺规作图,不写作法,保留作图痕迹);
(2)直线
与
相交于点O,且直线
,
所夹锐角
,求
的度数;
(3)在(2)的条件下,小颖得出
,请你运用所学知识判断小颖的结论是否正确,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ee6e1d480ece7117e1f87ebf4bbeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ee6e1d480ece7117e1f87ebf4bbeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25db870913249c9cd1c48e2bd2d2f6dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/24/8ad54631-6c59-4ef3-b5b4-f93b82942308.png?resizew=149)
(1)作出直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97cf714ffb3fd5917a76b191640b55fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95b4189edb86626a657f2d8a57154308.png)
(3)在(2)的条件下,小颖得出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53f382cb01b9ead4df16d21c3bd5c200.png)
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8 . 概念学习
规定:如果一个三角形的三个角分别等于另一个三角形的三个角,那么称这两个三角形互为“等角三角形”.
从三角形
不是等腰三角形
一个顶点引出一条射线与对边相交,顶点与交点之间的线段把这个三角形分割成两个小三角形,如果分得的两个小三角形中一个为等腰三角形,另一个与原来三角形是“等角三角形”,我们把这条线段叫做这个三角形的“等角分割线”.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/23/324d59fc-7e6e-471c-a751-e2cec1ad2f48.png?resizew=369)
(1)理解概念:判断下列说法是否正确(对的打√,错的打×)
①全等三角形是“等角三角形”()
②如图
,在
中,
,
,图中共有2对“等角三角形”()
③如图
,在
中,
,
,无论
为何值,
都不可能是
的“等角分割线”()
(2)概念应用:如图
,在
中,
为角平分线,
,
求证:
为
的等角分割线.
(3)在
中,
,
是
的等角分割线,直接写出
的度数.
规定:如果一个三角形的三个角分别等于另一个三角形的三个角,那么称这两个三角形互为“等角三角形”.
从三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/23/324d59fc-7e6e-471c-a751-e2cec1ad2f48.png?resizew=369)
(1)理解概念:判断下列说法是否正确(对的打√,错的打×)
①全等三角形是“等角三角形”()
②如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
③如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60742b466e878129b35628d21c2454ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)概念应用:如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c5840e0454fdec7d2158072c43b8db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f69e456af7ab8915434bb0bd2f5b3a24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a9afe4b588fccd34b74b0f765a7c7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
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2023-11-19更新
|
46次组卷
|
2卷引用:浙江省宁波市海曙区东恩中学2023-2024学年八年级上学期期中数学试题
9 . 在七年级的学习中,我们知道:(1)三角形的内角和等于
;(2)等腰三角形的两个底角相等.下面我们对这两点知识作进一步思考和探索.
(一)三角形的外角.
三角形内角的一条边与另一条边的反向延长线组成的角,称为三角形的外角.如图1,
就是
的
的外角.在三角形的每个顶点位置都可以找到它的外角,以
为例,我们探索外角与其它角的关系.
(①__________),
(②___________)
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a5a716592d862464b3ff814e45d0e11.png)
(③__________)
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/635b1af26e27be60f4cf4817e6d4e1d9.png)
由此我们得到了三角形外角的两条性质:
(1)三角形的一个外角等于和它不相邻的两个内角的和.
(2)三角形的一个外角大于任何一个和它不相邻内角.
问题1:
(1)请在以上括号①②③中填上适当的理由;
(2)请在图1中分别画出
和
的一个外角,并分别标注为
,
.
(二)等腰三角形的两个底角相等.
等腰三角形的两个底角相等,我们简述为“等边对等角”,数学小组据此提出问题:三角形中大边对的内角也大,即“大边对大角”正确吗?小聪同学进行了如下探索.
问题2:
如图2,
中
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b24a07ee331866778ea413e465a4f0ce.png)
证明:如图3,在
边上截取
,连接![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f7f05dfb173e003ab30d2a424b96637.png)
(④__________)
(整体大于部分)
又
(⑤_________)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/314df17ec77fb1e71d07c1c9cd9574d0.png)
由此说明三角形中大边对大角.
请在以上括号④⑤中填上适当的理由.
问题3:
如图4,
中
,
,请判断
是否成立,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e7a123c9cc0e058db28841fb0edcf3.png)
(一)三角形的外角.
三角形内角的一条边与另一条边的反向延长线组成的角,称为三角形的外角.如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b69d40b75d582c4b8ffa2369af1d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b69d40b75d582c4b8ffa2369af1d41.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/4/6ea8918a-30b6-42e6-8480-e3af911e746c.png?resizew=204)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4280c3963b4900adb983db9a3a4b58ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a1b09bae4841be75f196673a627497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ffc2f065a5d5febb87359016eac379d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a5a716592d862464b3ff814e45d0e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4d0f3991ab2d191e46e36e3072388b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d17adae48fae0dea0ab332763dc91e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/635b1af26e27be60f4cf4817e6d4e1d9.png)
由此我们得到了三角形外角的两条性质:
(1)三角形的一个外角等于和它不相邻的两个内角的和.
(2)三角形的一个外角大于任何一个和它不相邻内角.
问题1:
(1)请在以上括号①②③中填上适当的理由;
(2)请在图1中分别画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d57899ad4774aed9ccc7bd23db72153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/605f2976297a0deaa1602ef09d6a5afa.png)
(二)等腰三角形的两个底角相等.
等腰三角形的两个底角相等,我们简述为“等边对等角”,数学小组据此提出问题:三角形中大边对的内角也大,即“大边对大角”正确吗?小聪同学进行了如下探索.
问题2:
如图2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb980da8e86b4cfd322616dc84fc6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b24a07ee331866778ea413e465a4f0ce.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/4/dec32640-3e28-4f44-b8f0-5bafff271626.png?resizew=127)
证明:如图3,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc13fe21e64d9b45614ed43be847904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/4/aaa65144-a2b8-4e26-b3e4-7420e387dd04.png?resizew=128)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f7f05dfb173e003ab30d2a424b96637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d98228bd5ecb89ef69c62a71f8e1ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6818402824ac026a750a8bcc4c2db372.png)
又
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddd37e385a92dc12298ae8278cf58386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/314df17ec77fb1e71d07c1c9cd9574d0.png)
由此说明三角形中大边对大角.
请在以上括号④⑤中填上适当的理由.
问题3:
如图4,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e53497af8899cb299d762f1a4f46a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90c251ed1472ba56f13a80abbfeb06c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c9af7ab732d431dd78e84db9586d3cc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/4/f79f2beb-bbf5-4925-b9e3-721596dd078b.png?resizew=128)
您最近一年使用:0次
10 . 对于问题:过直线外一点作这条直线的垂线,小明和小亮给出两种不同的作法:
作法I:
(1)在直线
上任取一点
,连接
.
(2)以
为圆心,线段
的长度为半径作弧,交直线
于点
.
(3)分别以
,
为圆心,线段
的长度为半径作弧,两弧相交于点
.
(4)作直线
.直线
即为所求(如图1).
作法Ⅱ:如图2.
(1)以
为圆心,任意长为半径画弧,交直线
于
,
两点;
(2)连接
,作
的垂直平分线交
于点
;
(3)以
为圆心,
的长为半径画弧,交直线
于点
;
(4)作直线
,则直线
即为直线l的垂线
对于以上两个方案,判断正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/29/0dd6074d-e247-43ac-8742-37966cb4e4c8.png?resizew=184)
作法I:
(1)在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(3)分别以
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(4)作直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/29/71105851-b8c4-405c-9833-99bed97977d2.png?resizew=161)
作法Ⅱ:如图2.
(1)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(4)作直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/29/e7620042-1f44-40e8-b698-982fca1695eb.png?resizew=272)
对于以上两个方案,判断正确的是( )
A.方案I正确 | B.方案Ⅱ正确 | C.方案I、Ⅱ均正确 | D.方案I、Ⅱ均不正确 |
您最近一年使用:0次