6.3.1 角的概念 讲义（学生版+答案版） 2025-2026学年数学七年级上册人教版

INCLUDEPICTURE "节.tif" INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/节.tif" \* MERGEFORMAT INCLUDEPICTURE "../../节.tif" \* MERGEFORMAT INCLUDEPICTURE "../../节.tif" \* MERGEFORMAT INCLUDEPICTURE "../节.tif" \* MERGEFORMAT INCLUDEPICTURE "节.tif" \* MERGEFORMAT 6.3　角 6．3.1　角的概念 eq \o(\s\up7( INCLUDEPICTURE "知识梳理.tif" INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/知识梳理.tif" \* MERGEFORMAT INCLUDEPICTURE "../../知识梳理.tif" \* MERGEFORMAT INCLUDEPICTURE "../../知识梳理.tif" \* MERGEFORMAT INCLUDEPICTURE "../知识梳理.tif" \* MERGEFORMAT INCLUDEPICTURE "知识梳理.tif" \* MERGEFORMAT ),\s\do5(　　　　　　　)) 知识点一　角的认识 1．有公共端点的两条射线组成的图形叫作角，这个公共端点是角的顶点，这两条射线是角的两条边． 2．角也可以看作由一条射线绕着它的端点旋转而形成的图形． 练习1　下列图形中，能用∠O和∠1表示同一个角的是(　C　). eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX186.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX186.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX186.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX186.tif" \* MERGEFORMAT INCLUDEPICTURE "SX186.tif" \* MERGEFORMAT ),\s\do5(A)) 　　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX186A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX186A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX186A.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX186A.tif" \* MERGEFORMAT INCLUDEPICTURE "SX186A.tif" \* MERGEFORMAT ),\s\do5(B)) eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX186b.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX186b.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX186b.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX186b.tif" \* MERGEFORMAT INCLUDEPICTURE "SX186b.tif" \* MERGEFORMAT ),\s\do5(C)) 　　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX186C.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX186C.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX186C.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX186C.tif" \* MERGEFORMAT INCLUDEPICTURE "SX186C.tif" \* MERGEFORMAT ),\s\do5(D)) 【解析】要是能用∠1，∠O表示同一个角，必须共用角的顶点，且角的两边重合．选项A，B，D中，以O为顶点的角不止一个，用∠O表示不明确，不符合题意；选项C符合题意，故选C. 总结　角的表示：①用三个大写字母可以表示任一角(顶点字母在中间)；②用一个顶点字母表示角的前提是以该点作为顶点的角只有一个；③用数字或希腊字母表示角时，要在靠近角的顶点处画上弧线，并标上数字或希腊字母． 知识点二　角的单位与换算 3．以度、分、秒为单位的角的度量制，叫作角度制． 4．1周角＝360°＝2平角，1平角＝180°＝2直角，1直角＝90°，1°＝60′，1′＝60″. 练习2　把12°15′36″用度表示正确的是(　B　). A．12.11° B．12.26° C．12.16° D.11.26° 【解析】因为1′＝60″， 所以36″＝0.6′. 因为1°＝60′， 所以15.6′＝0.26°， 所以12°15′36″＝12.26°.故选B. 总结　在进行单位换算时，把高级单位转化为低级单位，要乘进率，把低级单位转化为高级单位，要除以进率． 知识点三　方向角 5．方向角通常用南偏东多少度，南偏 ... ...