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单击此处编辑母版标题样式,单击此处编辑母版文本样式,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,单击此处编辑母版标题样式,单击此处编辑母版文本样式,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,4.3,角,4.3.3 余角和补角,R,七年级上册,新课导入,如图坝底是由石块堆积而成，要测出,1,的度数，聪明的你有什么简单的方法吗？,要解决这问题，我们先来学习,4.3.3,余角和补角,.,学习目标,（,1,）弄清楚余角、补角的意义及其性质,.,（,2,）运用余角、补角的性质解决一些简单的问题,.,（,3,）会根据方位角确定物体的方位,.,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,推进新课,余角和补角的定义,知识点,1,问题,根据你的理解，如何定义余角？,如果两个角的和等于,90,（直角），就说这两个角,互为余角,，即其中每一个角是另一个角的余角,.,90,问题,类比余角的定义，怎么定义补角？,如果两个角的和等于,180,（平角），就说这两个角,互为补角,，即其中一个角是另一个角的补角,.,180,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,思考,1.,定义中的“互为”是什么意思？,2.,把下图中,1,与,ADF,分离并多次变换位置，如图，这两角还是互为补角吗？,1,A,D,F,1,1,即每一个角都是另一个角的余角（补角）,已知,是锐角，则,的余角可表示为,，,的补角可表示为,.若,的补角是它的3倍，则,=,.,1,90-,180,-,补充,45,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,2,已知,1,与,3,互补，,2,与,4,互补,.,若,1,2,，那么,3,和,4,相等吗？为什么？,补充,1与3互为补角，2与4互为补角，1=2,那么3=180-1,4=180-2,，,所以3=4.,3,已知,1,与,2,，,3,都互为补角,.,那么,2,和,3,的大小有什么关系？,补充,由,1,与,2,和,3,都互为补角，,那么,2,180,1,，,3,180,1,，,所以,2,3.,小结,等角 的余角相等,.,等角 的补角相等,.,（同角）,（同角）,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,强化练习,互为余角：,10,和,80,，,30,和,60,；互为补角：,10,和,170,，,30,和,150,，,60,和,120,，,80,和,100,.,图中给出的各角中，哪些互为余角？哪些互为补角？,余角和补角的运用,知识点,2,例,如图，,A,，,O,，,B,在同一直线上,射线,OD,和射线,OE,分别平分,AOC,和,BOC,，图中哪些角互为余角,？,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,分析：,要找图中互余的角，就是要找和为,度的两个角.,90,所以,COD,+,COE,解：因为,A,，,O,，,B,在同一直线上，所以,AOC,和,BOC,互为补角,.,又因为射线,OD,和射线,OE,分别平分,AOC,、,BOC,，,90,(,AOC,+,BOC,),状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,思考,观察本例的图形，除了,AOC,与,BOC,互补外，还有哪些角互为补角？,所以，,COD,和,COE,互为余角，,同理，,AOD,和,BOE,，,AOD,和,COE,，,COD,和,BOE,也互为余角,.,AOD,和,DOB,AOE,和,EOB,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,例,如图，货轮,O,在航行过程中，发现灯塔,A,在它南偏东,60,的方向上，同时，在它北偏东,40,、南偏西,10,、西北,(,即北偏西,45,),方向上又分别发现了客轮,B,，,货轮,C,和海岛,D,.,仿照表示灯塔方位的方法，画出表示客轮,B,、货轮,C,和海岛,D,方向的射线,.,O,东,南,西,北,A,60,40,B,C,10,45,D,灯塔,A,在货轮,O,的南偏东60方向上，反过来，货轮,O,在灯塔,A,的什么方向上?,补充,北偏西60,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,强化练习,如图，射线,OA,表示的方向是,，,射线,OB,表示的方向是,或,，,射线,OC,表示的方向是,.,北偏西30,南偏西45,西南方向,南偏东70,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,随堂演练,1.,下列说法不正确的是（）,A.任意两直角互补,B.任意两锐角互余,C.同角或等角的补角相等,D.同角或等角的余角相等,B,2.,下列结论正确的个数为（）,互余且相等的两个角都是45,锐角的补角一定是钝角,一个角的补角一定大于这个角,一个锐角的补角比这个角的余角大90,A.1个,B.2个C.3个D.4个,C,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,课堂小结,如果两个角的和等于,90,（直角），就说这两个角,互为余角,，即其中每一个角是另一个角的余角,.,90,如果两个角的和等于,180,（平角），就说这两个角,互为补角,，即其中一个角是另一个角的补角,.,180,课堂小结,1.,同学们，今天你学到了什么呀？和同桌说说有什么收获。,2.,师生共同总结反思学习情况。,课后作业,1.,从课后习题中选取；,2.,完成练习册本课时的习题,.,谢谢观赏！,再见！,
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