2022年中考数学必考知识点三角形 .pdf
名师整理精华知识点中考数学必考知识点三角形知识点回顾：（一）三边关系：三角形的任意两边之和大于第三边（二）内角与外角：三角形三个内角的和为180；直角三角形的两个锐角互余；三角形的一个外角等于与它不相邻的两个内角的和；n 边形的内角和等于(n-2)180；任意多边形的外角和等于360。（三）特殊线段：三角形的中线、高线、角平分线都是_(线段、射线、直线)_叫三角形的中位线中位线的性质：_（四）三角形的分类：1三角形按角分为_，_，_2三角形按边分为_,_（五）三角形的内心是_，外心是 _，重心是 _，垂心是 _。知识点一：三角形三边关系三角形中任意两边之和_第三边。例 1：选择题：（1）（2009 黑龙江大兴安岭）如图，为估计池塘岸边A、B两点的距离，小方在池塘的一侧选取一点O，测得15OA米，10OB米，A、B间的距离不可能是（）A5 米B 10 米C 15 米D20 米【解】由ABABAB151010151510得到 5AB25 所以，答案：A（2）（20XX年湖南长沙）已知三角形的两边长分别为3cm和 8cm，则此三角形的第三边的长可能是（）A4cm B5cm C6cm D 13cm 名师整理精华知识点答案：C同步检测一：1(20XX 年温州)下列长度的三条线段能组成三角形的是()A 1cm，2cm，3 5cm B4cm，5cm，9cm C5cm，8cm，15cm D6cm，8cm，9cm 2.（20XX年崇左）一个等腰三角形的两边长分别为2 和 5，则它的周长为（）A7 B9 C12 D9或 12 3.（07 深圳）已知三角形的三边长分别为3、8、x，若 x 的值为偶数，则x 的值有（）A.6个 B.5个 C.4 个 D.3个【答案】1D，2C，3D。知识点二：三角形的内角和外角三角形的 3 个内角和为 _，外角与不相邻内角的关系：_。例 2：(1)（07 济南）已知一个三角形三个内角度数的比是1:5:6，则其最大内角度数为（）A.60 B.75 C.90 D.120【解】设其中的一份为x,根据三角形的 3 个内角和为1800 得到 x+5x+6x=1800 所以 x=150,最大内角度数为90答案：C(2)（09 娄底）如图 1，已知ACED，C=26，CBE=37，则BED的度数是 ()A63B83C73D53【解】因为 AC ED 所以CAEBED因为CA是ABC的外角，所以000633726CBECCAE所以BED=63答案：A 同步检测二：4.（20XX年广西梧州）如图，ABC中，A60，C40，延长CB到D，则ABD度5.如图，在 ABC中，D是 BC边上一点，1=2，3=4，BAC=63 求 DAC的度数【答案】4.1000 ，5.240 A B C D 4321DCBA文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5名师整理精华知识点知识点三：三角形的中线、高线、角平分线，直角三角形的两个锐角互余。如图，在 ABC中，AD是高线，AE是角平分线，AF中线.则(1)ADC 90；(2)CAE 12；(3)CF 12；例 3 如图，AD、AF分别是 ABC的高和角平分线，已知 B=36，C=76，则DAF=_ 度【解】AD是 ABC的高，所以090ADC，090CADC，000147690CADAF是 ABC的角平分线，所以000034)7636180(2121BACFACDAF=000201434CADFAC例 4如图，在ABC中，AABC与ACD的平分线交于点A1，得A1；A1BC与A1CD的平分线相交于点A2，得A2；A2008BC与A2008CD的平分线相交于点A2009，得A2009则A2009【解】：根据外角的性质A=ACD-ABC,A1=A1CD-A1BC,而且ACD=2A1CD，ABC=2 A1BC，所以A=2A1，同理A1=2A2，以此类推.答案：20092知识点四：多边形的内角和外角 n 边形的内角和等于_；任意多边形的外角和等于_。例 5（20XX年龙岩市）一个凸多边形的内角和与外角和相等，它是边形。答案：4 随堂检测：1（2009山西太原市）如果三角形的两边分别为3 和 5，那么连接这个三角形三边中点所文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5名师整理精华知识点得的三角形的周长可能是（）A4 B4.5 C5 D 5.5 2（2009福建龙岩市）将一副三角板按图中方式叠放，则角等于（）A30B45C60D753（2009辽宁铁岭市）如图所示，已知直线ABCD，125C，45A，则E的度数为（）A70B 80C90D1004.(20XX 年达州)长度为2、3、4、5 的四条线段，从中任取三条线段能组成三角形的概率是 _.5.在 ABC 中，若 A C13 B，则 A，B，这个三角形是 .6.(20XX年扬州市)一副三角板如图所示叠放在一起，则图中的度数是 _。7（20XX年湖北十堰市）下列命题中，错误的是（）A三角形两边之和大于第三边B三角形的外角和等于360C三角形的一条中线能将三角形面积分成相等的两部分D等边三角形既是轴对称图形，又是中心对称图形文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5名师整理精华知识点8.如图，ABC中，A=40,B=72，CE平分 ACB，CD AB于 D，DFCE，则CDF=度.EDCBAF9.（20XX年沈阳市）已知ABC中，60A，ABC，ACB的平分线交于点O，则BOC的度数为10.如图,要在河边修建一个水泵站,分别向张村,李村送水修在河边什么地方,可使所用的水管最短?(写出已知,求作,并画图)答案：1.D 2.D 3.B 4.34 5.360，1080，钝角三角形 6.750 7.D8.解0000687240180ACB，03421ACBBCE，001890BBCD000161834DCE，007490DCECDF9.解)180(211802121180000AACBABCBOC=900+A21=1200 10.作法：（1）作点 A关于直线a 的对称点A（2）连结 AB 交 a 于点 C则点 C就是所求的点证明：在直线a 上另取一点C,连结 AC,AC,AC,CB直线 a 是点 A,A 的对称轴,点 C,C 在对称轴上AC=AC,AC=ACAC+CB=AC+CB=AB 在 ACB 中,AB AC+CB AC+CB AC+CB 即 AC+CB 最小文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5文档编码:CK1M5J3B10S4 HM3I9T4I1M4 ZS9S5N1M1L5
