2022年平行线与相交线的知识点总结与归纳2 .pdf

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1、平行线与相交线（1）一、知识概述（一）从台球桌面上得角，引出有关角得概念1、两角互余、互补得概念及性质（1）定义：如果两个角得与就是180，那么这两个角互为补角、（如图）简称互补、如果两个角得与就是90，那么这两个角互为余角、（如图）简称互余、说明：互余、互补就是指两个角得关系、互补或互余得两个角，只与它们得与有关，而与其位置无关、用数学语言表述为：若=180，则与互补；反之，若与互补，则=180、若=90，则与互余；反之若与互余，则=90、（2）性质：同角或等角得补角相等、同角或等角得余角相等、2、对顶角得概念（1）如果一个角得两边分别就是另一个角得两边得反向延长线，这样得两个角叫做对顶角、

2、如图中得 1 与 3，2 与 4 就是对顶角、由对顶角得位置特点也可将其描述为：两条直线相交成四个角，其中不相邻得两个角叫做对顶角、一个角得两边分别就是另一个角得两边得反向延长线，这两个角叫做对顶角、说明：只有两条直线相交时，才能产生对顶角，对顶角就是成对出现得、对顶角得本质特征就是：两个角有公共顶点，其两边互为反向延长线、（2）对顶角得性质：对顶角相等、（二）探索直线平行得条件1、两条直线相交构成四个有公共顶点得角、一条直线与两条直线相交得八个角，简称“三线八角”，则不共顶点得角得位置关系有同位角、内错角、同旁内角、如图所示，直线 AB、CD被直线 EF所截，形成了8 个角、（1）同位角：两

3、个角都在两条直线得同侧，并且在第三条直线（截线）得同旁，这样得一对角叫做同位角、如 1 与 5，3 与 7，4 与 8，2 与 6、（2）内错角：两个角都在两条直线之间，并且在第三条直线（截线）得两旁，这样得一对角叫做内错角、例如 3 与 5，4 与 6、（3）同旁内角：两个角都在两条直线之间，并且在第三条直线（截线）得同旁，这样得一对角叫做同旁内角、例如 4 与 5，3 与 6、2、两条直线平行得条件：两条直线被第三条直线所截，如果（1）同位角相等，两直线平行、（2）内错角相等，两直线平行、（3）同旁内角互补，两直线平行、二、重难点知识剖析1、互为补角与互为邻补角得关系、互为补角就是两个角得

4、与为 180，与它们得位置无关、而互为邻补角既与它们得与为 180 有关，又与位置有关，不要混淆、2、灵活运用互余、互补等知识点以及对顶角得性质列方程求解，即学会用代数法解几何题得方法、3、证明两直线平行时，必须弄清所用条件中得同位角、内错角、同旁内角就是哪两条直线被哪一条直线所截而成得，因为推出得结论就是除截线外得另两条直线平行、文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX

5、6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C

6、2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT

7、3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9

8、V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7

9、ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V

10、2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文

11、档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6平行线与相交线（2）一、知识概述1、平行线得特征特征一：两条平行线被第三条直线所截，同位角相等，简单说成“两直线平行，同位角相等”，使用方法如图：a b，1=2（两直线平行，同位角相等）特征二：两直线平行，内错角相等、使用方法：a b，2=3（两直线平行，内错角相等）特征三：两直线平行，同旁内角互补、使用方法：a b，2 4=180（两直线平行，同旁内角互补）2、直线平行得条件与平行线得特征得区分表3、尺规作图得意义在几何里，把限

12、定用直尺与圆规来画图，称为尺规作图。虽然尺规也就是画图工具，但尺规作图不同于用工具画图，尺规作图只限于用无刻度得直尺与圆规，直尺用于根据两点得位置作直线、射线、线段或作延长线，圆规用于根据圆心位置、半径大小作弧或圆。所以作图题都应用直尺或圆规作图，而不能把用三角尺画直角、画平行线等当作尺规作图。本节课要求会利用尺、规作线段与一个角等于已知角等。二、重难点知识剖析1、（1）同位角相等、内错角相等、同旁内角互补，都就是平行线特有得性质，切不可忽略前提条件：“两直线平行”。当两直线不平行时，同位角、内错角就不相等，同旁内角不互补。（2）只要两条直线被第三条直线所截，都存在同位角、内错角，但不一定相等

13、，同旁内角不一定互补。2、要分清平行线得识别与平行线得特征之间得关系，不要混淆运用，同时要学会综合运用这两者之间都就是存在着“位置关系”与“数量关系”，其中由“数量关系”去确定“位置关系”就是平行线得识别方法与过程，反之就是平行线得特征。文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C

14、2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT

15、3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9

16、V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7

17、ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V

18、2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文

19、档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX

20、6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H63、用尺、规作线段与角时，要学会叙述几何作图语言，如过点作直线与直线平行，或以点为圆心，以为半径作弧，等等。文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文

21、档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX

22、6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C

23、2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT

24、3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9

25、V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7

26、ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6文档编码:CX6Y1V6C2W3 HT3Z10K9V10G7 ZH5Q8V2M8H6