1 . 相传墨翟以木头制成木鸟,研制三年而成,是人类最早的风筝起源.如图所示的风筝骨架中,
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49abceacaa34448ac572cba0bf2032ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc310194575262fb45352c2fbc19868.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 如图,直线
,
所成的角跑到画板外面去了,量出图中
,
,就能求出直线
,
所成的角为________ 度.
![](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/9ee4e0de0c1de0835766b7f627f348c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54eb639802989aa4b8e541734ec00f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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3 . 如图,直线
、
相交于点O,
平分
,
,
与
的度数之比为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc310194575262fb45352c2fbc19868.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e7b8a59f8d66176463f3d71f882a26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e75a7b0ab537e7e786f25cb8d6888293.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b69d40b75d582c4b8ffa2369af1d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/605f2976297a0deaa1602ef09d6a5afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c60fe5130254a1d38bb4fd0015630f6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc310194575262fb45352c2fbc19868.png)
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4 . 下列说法:①三角形的高、中线、角平分线都是线段;
②垂直于同一条直线的两条直线互相平行;
③两条直线被第三条直线所截,同位角相等;
④“对顶角相等”的证明依据是等角的补角相等.
其中正确的有( )个.
②垂直于同一条直线的两条直线互相平行;
③两条直线被第三条直线所截,同位角相等;
④“对顶角相等”的证明依据是等角的补角相等.
其中正确的有( )个.
A.1 | B.2 | C.3 | D.4 |
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5 . 综合与实践
【问题情境】在数学综合与实践课上,老师让同学们以“三角板与平行线”为主题开展数学活动.已知直线
,在直角三角板
中,
.
【操作发现】(1)如图1所示,将直角三角板
顶点A放在直线
上,设边
与
相交于点
,边
与
相交于点
.当
时,发现
.请说明理由.
【深入探究】(2)如图2所示,将图1中三角板
的直角顶点
放在平行线
和
之间,两直角边
,
分别与
,
相交于点
和
,得到
和
,试探究
和
的数量关系并说明理由.以下是小刚和小红两位同学的解题思路:
小刚:过点
作
和
其中一条直线的平行线,再利用平行线的有关知识就能解决问题:
小红:连接
,再利用平行线性质与三角形内角和等于
的知识相结合,就能解决问题.
请你帮助其中一位同学书写完整的解题过程,或用其它方法解决.
【拓展运用】(3)受小刚和小红的启发,同学们继续探究以下问题,在(2)的情况下,分别作
和
对顶角的角平分线,它们相交于点
,如图3所示,请直接写出
的度数.
【问题情境】在数学综合与实践课上,老师让同学们以“三角板与平行线”为主题开展数学活动.已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e03566282ef39ad17821036f228174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
【操作发现】(1)如图1所示,将直角三角板
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a4df52c7b7ba685c4bf50cde19025a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20e950be3dc00f34e69bc80c6ca4dfe6.png)
【深入探究】(2)如图2所示,将图1中三角板
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b69d40b75d582c4b8ffa2369af1d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d57899ad4774aed9ccc7bd23db72153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b69d40b75d582c4b8ffa2369af1d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d57899ad4774aed9ccc7bd23db72153.png)
小刚:过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
小红:连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e7a123c9cc0e058db28841fb0edcf3.png)
请你帮助其中一位同学书写完整的解题过程,或用其它方法解决.
【拓展运用】(3)受小刚和小红的启发,同学们继续探究以下问题,在(2)的情况下,分别作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b69d40b75d582c4b8ffa2369af1d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d57899ad4774aed9ccc7bd23db72153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10aa98b163ade82dcadbe8dd3b73e42e.png)
您最近一年使用:0次
6 . 如图,直线
,
,
相交于点
,且
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5324ce5fd43c5b05e8fad764880f7b3.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/057cdb4057bca398a838e868efd360f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619966af5abba968962c958a9facb22e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5324ce5fd43c5b05e8fad764880f7b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83873a9d782f2588c5eedbfe73f9bc2f.png)
您最近一年使用:0次
7 . 如图.直线
和直线
相交于点
,若
,则
的度数是( )
![](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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c9c14d7ac0501707e8d6eb48a956faa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d57899ad4774aed9ccc7bd23db72153.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
8 . 如图所示,直线
与直线
相交于点
平分
,
.
,求
的度数;
(2)猜想
与
之间的位置关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0b90b22cfb3045d93a9857ef7549d16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/778d3556c2454a733a15629af5c2444f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f22679df3b30ca4564305b434de71a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b1ff9c5153d90cfb60a99395ab6294.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbee6d5731d6f4bb1e4f2ba3d89b7dc.png)
(2)猜想
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
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9 . 如图,直线
与
交于点
,已知
和
位于
的两侧,且
,
平分
,若
,求
的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a49bdf1dcfe6c344dd2442669e72c44b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22df2977de56cc69be0c1e847653d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b571c587a699f24c1121b09d54f3f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/418ebb89d29f4f631b055c911e8d178a.png)
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7日内更新
|
135次组卷
|
5卷引用:安徽省六安市金安区六安市轻工中学2022-2023学年七年级下学期期末数学试题
安徽省六安市金安区六安市轻工中学2022-2023学年七年级下学期期末数学试题(已下线)第02讲 垂直(4个知识点+3类热点题型讲练+习题巩固)-【帮课堂】2023-2024学年七年级数学下册同步学与练(人教版)广东省东莞市光明中学2023-2024学年七年级下学期期中数学试题(已下线)专题10相交线与平行线的判定8种常考题型归类【好题汇编】-备战2023-2024学年七年级数学下学期期末真题分类汇编(安徽专用)(已下线)专题03+相交线与平行线1(含平行模型)(10大题型+优选提升题)-备战2023-2024学年七年级数学下学期期末真题分类汇编(北师大版)
10 . 下列说法正确的是( )
A.同位角相等 | B.同角的补角相等 |
C.相等的角是对顶角 | D.两直线平行,同旁内角相等 |
您最近一年使用:0次
7日内更新
|
45次组卷
|
2卷引用:四川省达州市达川区达川区铭仁园学校2023-2024学年八年级下学期期中数学试题