4.1成比例线段(一).pdf

1 第四章图形的相似1成比例线段(一)山东省青岛实验初级中学纪戌栋一、学生知识状况分析相似图形是现实生活中广泛存在的现象，在小学时学生就接触过比例的知识，在七年级下册时学生已学习了全等图形（其实全等图形就是相似图形的一个特例）。所以学生已经具备一些知识基础、活动经验基础等，学生在学习线段的比时不会感到很困难。二、教学任务分析（一）教学知识点1、了解相似形、线段的比概念；2、会求两条线段的比,应用线段的比解决实际问题。（二）能力训练要求通过现实情境，进一步发展学生从数学的角度提出问题、分析问题和解决问题的能力，培养学生的数学应用意识，体会数学与自然、社会的密切联系。（三）情感与价值观要求1、有关比例的计算，让学生懂得数学在现实生活中的作用，从而增强学生学好数学的信心；2、通过解答实际问题，激发学生学数学的兴趣，增长社会见识；3、在与他人的共同探索、讨论问题的过程中，增强合作交流的意识。2 教学重点：理解线段比的概念及其求解。教学难点：求线段的比，注意线段长度单位要统一。教学方法：探索、发现法教学准备：多媒体课件三、教学过程分析本节课设计了六个教学环节：第一环节：设置情境，引入新课；第二环节：新课讲解；第三环节：随堂练习；第四环节：想一想；第五环节：回顾与思考；第六环节：布置作业。第一环节设置情境，引入新课活动内容：通过用幻灯片展示生活的的图片，引入本章的学习内容相似图形。活动目的：引发学生思考相似图形的特征，激发学生的学习兴趣。实际效果：学生们都很兴奋，对学习充满了好奇心。第二环节：新课讲解活动内容：1.请在下面图形中找出形状相同的图形？你发现这些形状相同的图形有什么不同？文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P93 2.引入线段的比:如果选用同一个长度单位量得两条线段AB,CD的长度分别是 m，n,那么就说这两条线段的比（ratio）AB:CD=m:n,或写成nmCDAB其中,AB,CD 分别叫做这个线段比的前项和后项.如果把nm表示成比值 k,那么kCDAB,或 AB=k CD.两条线段的比实际上就是两个数的比。五边形 ABCDE 与五边形 ABCDE形状相同，AB=5cm，AB=3cm。AB:AB=5:3，就是线段 AB与线段 AB的比。这个比值刻画了这两个五边形的大小关系。3.想一想：两条线段长度的比与所采用的长度单位有没有关系？通过上面的活动学生应该对这个问题有了一定的认识:两条线段长度的比与所采用的长度单位无关.但要采用同一个长度单位.4.做一做：如图，设小方格的边长为1，四边形 ABCD 与四边形 EFGH 的顶点都在格点上，那么AB，CD，EH，EF的长度分别是多少？分别计算值。EFEHADABEFADEHAB,文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P94 你发现了什么？四条线段 a，b，c，d 中，如果 a 与 b的比等于 c 与 d 的比，即 a/b=c/d，那么这四条线段 a，b，c，d 叫做成比例线段，简称比例线段.上图中 AB,EH,AD,EF是成比例线段，AB,AD,EH,EF也是成比例线段。5.议一议：如果 a,b,c,d四个数成比例，即 a/b=c/d，那么 ad=bc吗？反过来如果 ad=bc，那么 a,b,c,d四个数成比例吗？比例的基本性质如果 =,那么 ad=bc。如果 ad=bc(a,b,c,d都不等于零)，那么 =。6.例题 1：如图，一块矩形绸布的长AB=am,AD=1m，按照图中所示的方式将它裁成相同的三面矩形彩旗，且使裁出的每面彩旗的长与宽的比与原绸布的长与宽的比相同，即 ,那么 a 的值应当是多少？活动目的：通过发现这些形状相同的图形的不同点，引出线段的比的概念，中学生实际操作后并进行了讨论得出：两条线段长度的比与所采用的长度单位没有关系。并引入成比例线段的概念。再通过教科书上的例题，让学生利用所学的知识来解决实际生活中的问题。活动效果:学生在动手操作实践中掌握了知识，并有效地攻克了本节课的重点、难点。第三环节：随堂练习活动内容：1、一条线段的长度是另一条线段长度的5 倍，则这两条线段之比是_badcbadcABADADAE文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P95 2、一条线段的长度是另一条线段长度的53，则这两条线段之比是 _ 3、已知 a、b、c、d 是成比线段,a=4cm,b=6cm,d=9cm,则 c=_ 4、如果yx52，那么yx=_ 5、把pqmn写成比例式，写错的是（）6、已知 a:b:c=2:3:4,且 a+b+c=15，则 a=_,b=_,c=_.活动目的：让学生巩固课堂上所学的知识。活动效果：学生基本都能运用所学的知识解决比例问题，收到了较好的教学效果。第四环节：想一想活动内容：生活中还有哪些利用线段比的事例?你能举例吗？房屋装修平面图，手机模型，汽车模型，深圳世界之窗，建筑物的效果图等等。活动目的：进一步让学生体会线段的比在生活中的应用。活动效果：活动中学生们很活跃，例举了很多例子，比如：地图、指示图、等等。第五环节：回顾与思考活动内容：这节课我们学习了哪些知识?你有什么收获?你有什么发现、探索?活动目的：让学生回顾本节课的学习内容，学会归纳，善于总结，做一个有心人。npqmA.qnmpB.pnmqC.qpnmD.文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 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HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P96 活动效果：虽然学生的程度不同，但不同程度的学生都能够有所收获。学生回答不完整的，再由老师补充小结：1）、线段的比的概念、表示方法；前项、后项及比值k；2）、两条线段的比是有序的;与采用的单位无关，但要选用同一长度单位；3）、两条线段的比在实际生活中的应用。第六环节：布置作业作业:略。四、教学反思1、教师可以根据学生的实际情况进行适当调整，设置出适合个人教学的情境。书上的情境设置应该是适用于广大地区的，老师也可以根据自己身边的熟悉的事物来设置情境，或是就用教科书上的情境。具有地方特色的教学资源，不仅丰富了学生对家乡风景的认识和了解，也上学生感受到数学知识在生活中的应用。2、教学中穿插了让同桌之间用不同的单位测量课本的长与宽(精确到 0.1cm),并求出这两条线段的长度之比。添加这个环节目的是对学生得出“两条线段长度的比与所采用的长度单位无关”的结论埋下伏笔。学生已经有了全等图形和比例的知识作为铺垫，生活中也存在大量相似图形的例子，所以学生学习起来不会很难，可以大胆的放手让学生自己去动手操作、动脑思考，老师可以在适当的时候给予帮助和补充。3、教材上的例题可以交给学生自学，然后通过随堂联系加以巩固。如果不能达到预期效果，时间允许的话可以补充相关的练习。文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 ZO9T6R8J9P9文档编码:CW2V1Z6Q3D1 HF5R6S8Q5L8 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