最新八年级上册数学知识点总结1优秀名师资料.doc
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1、八年级上册数学知识点总结1第一章 三角形的初步知识 复习总目 1、掌握三角形的角平分线、中线和高线 2、理解三角形的两边之和大于第三边的性质 3、掌握三角形全等的判定方法 知识点概要 1、 三角形的定义:由不在同一直线上的三条线段首尾顺次相接组成的图形叫做三角形. 三角形有三条边,三个内角,三个顶点.组成三角形的线段叫做三角形的边;相邻两边所组成的角叫做三角形的内角; 相邻两边的公共端点是三角形的顶点, 三角形ABC用符号表示为?ABC,三角形ABC的边AB可用边AB所对的角C的小写字母c 表示,AC可用b表示,BC可用a表示. 注意:(1)三条线段要不在同一直线上,且首尾顺次相接; A_ (
2、2)三角形是一个封闭的图形; (3)?ABC是三角形ABC的符号标记,单独的?没有意义( 2、 三角形的分类: (1)按角分类: _B C_ 直角三象形 三角形 锐角三角形斜三角形 钝角三角形 (2)按边分类: 底边和腰不相等的等腰三角形 等腰三角形 三角形 等边三角形 不等边三角形 3、 三角形的主要线段的定义: (1)三角形的中线 三角形中,连结一个顶点和它对边中点的线段( A表示法:1.AD是?ABC的BC上的中线. 12.BD=DC=BC. 2注意:?三角形的中线是线段; BCD?三角形三条中线全在三角形的内部; advantages, facing the Yangtze River
3、 Delta, Pearl River Delta, Shandong peninsula, Beijing-Tianjin-Tangshan area, targeted investment promotion several times. Industry-led unit and various town streets are developing detailed promotion plans, the basis of what is specific to each industry, has formed a kind of scale, need to bring in
4、the kind of projects each town street has the kind of resources, what location, focus on the development of the kind of industries. Four stroke technology and science. Determinants of technology is the Countys economic development through scientific and technological innovation, improve product valu
5、e-added and improve economic competitiveness, is the inevitable way to achieve leapfrog development. Talent is the city center citys first resource, is the primary industry development, and revitalization of the social protection. So, in terms of skills: to catch . Competitive. Encouraging enterpris
6、es to actively undertake science and technology projects, strengthening research cooperation, using advanced technology to increase the added value of their products to ensure that introduction of transforming scientific and technological achievements during the year . . New research enterprises . .
7、 Home, creating innovative platforms . . Generic classifier. In: first, we must strengthen the cultivation of talent, efforts to increase vocational education and training and meet the basic demand of enterprise development. Then introduced a number of the county needed scarce education, health prof
8、essionals, meet social development needs to invest more in machinery, pharmaceutical manufacturing research and development in higher education, such as the introduction of talent to meet the need. Third, we must rely on . . Post-doctoral workstation, . . Food research station platform, to the XX Un
9、iversity to find experts ?三角形三条中线交于三角形内部一点; ?中线把三角形分成两个面积相等的三角形( (2)三角形的角平分线 A三角形一个内角的平分线与它的对边相交,这个角顶点与交点之间的线段 21表示法:1.AD是?ABC的?BAC的平分线. 12.?1=?2=?BAC. BCD2注意:?三角形的角平分线是线段; ?三角形三条角平分线全在三角形的内部; ?三角形三条角平分线交于三角形内部一点; ?用量角器画三角形的角平分线( (3)三角形的高 A从三角形的一个顶点向它的对边所在的直线作垂线,顶点和垂足之间的线段( 表示法:1.AD是?ABC的BC上的高线. 2.A
10、D?BC于D. 3.?ADB=?ADC=90?. BDC注意:?三角形的高是线段; ?锐角三角形三条高全在三角形的内部,直角三角形有两条高是边,钝角三角形有两条高在形外; ?三角形三条高所在直线交于一点( 、三角形的三边关系 4三角形的任意两边之和大于第三边;任意两边之差小于第三边. 注意:(1)三边关系的依据是:两点之间线段是短; (2)围成三角形的条件是任意两边之和大于第三边( 5、 三角形的角与角之间的关系: (1)三角形三个内角的和等于180:; (2)三角形的一个外角等于和它不相邻的两个内角的和; (3)三角形的一个外角大于任何一个和它不相邻的内角. (4)直角三角形的两个锐角互余.
11、 6、三角形的稳定性: 三角形的三边长确定,则三角形的形状就唯一确定,这叫做三角形的稳定性( 注意:(1)三角形具有稳定性; (2)四边形没有稳定性. 7、全等三角形 (1)全等三角形的概念 能够完全重合的两个三角形叫做全等三角形。 (2)三角形全等的判定 advantages, facing the Yangtze River Delta, Pearl River Delta, Shandong peninsula, Beijing-Tianjin-Tangshan area, targeted investment promotion several times. Industry-led
12、 unit and various town streets are developing detailed promotion plans, the basis of what is specific to each industry, has formed a kind of scale, need to bring in the kind of projects each town street has the kind of resources, what location, focus on the development of the kind of industries. Fou
13、r stroke technology and science. Determinants of technology is the Countys economic development through scientific and technological innovation, improve product value-added and improve economic competitiveness, is the inevitable way to achieve leapfrog development. Talent is the city center citys fi
14、rst resource, is the primary industry development, and revitalization of the social protection. So, in terms of skills: to catch . Competitive. Encouraging enterprises to actively undertake science and technology projects, strengthening research cooperation, using advanced technology to increase the
15、 added value of their products to ensure that introduction of transforming scientific and technological achievements during the year . . New research enterprises . . Home, creating innovative platforms . . Generic classifier. In: first, we must strengthen the cultivation of talent, efforts to increa
16、se vocational education and training and meet the basic demand of enterprise development. Then introduced a number of the county needed scarce education, health professionals, meet social development needs to invest more in machinery, pharmaceutical manufacturing research and development in higher e
17、ducation, such as the introduction of talent to meet the need. Third, we must rely on . . Post-doctoral workstation, . . Food research station platform, to the XX University to find experts 三角形全等的判定定理: (1)边角边定理:有两边和它们的夹角对应相等的两个三角形全等(可简写成“边角边”或“SAS”) (2)角边角定理:有两角和它们的夹边对应相等的两个三角形全等(可简写成“角边角”或“ASA”) (3
18、)边边边定理:有三边对应相等的两个三角形全等(可简写成“边边边”或“SSS”)。 直角三角形全等的判定: 对于特殊的直角三角形,判定它们全等时,还有HL定理(斜边、直角边定理):有斜边和一条直角边对应相等的两个直角三角形全等(可简写成“斜边、直角边”或“HL”) (3)全等变换 只改变图形的位置,不改变其形状大小的图形变换叫做全等变换。 全等变换包括一下三种: (1)平移变换:把图形沿某条直线平行移动的变换叫做平移变换。 (2)对称变换:将图形沿某直线翻折180?,这种变换叫做对称变换。 (3)旋转变换:将图形绕某点旋转一定的角度到另一个位置,这种变换叫做旋转变换。 中考规律盘点及预测 三角形
19、的两边之和大于第三边的性质历年来是经常考到的填空题的类型,三角形角度的计算也是考到的填空题的类型,三角形全等的判定是很重要的知识点,在考试中往往会考到。 第二章 特殊三角形 复习总目 1、掌握等腰三角形的性质及判定定理 2、了解直角三角形的基本性质 2、掌握勾股定理的计算方法 知识点概要 1、图形的轴对称性质:对称轴垂直平分连接两个对称点的线段;成轴对称的两个图形是全等图形 2、等腰三角形的性质 (1)等腰三角形的性质定理及推论: 定理:等腰三角形的两个底角相等(简称:等边对等角) 推论1:等腰三角形顶角平分线平分底边并且垂直于底边。即等腰三角形的顶角平分线、底边上的中线、底边上的高重合。 推
20、论2:等边三角形的各个角都相等,并且每个角都等于60?。 3、三角形中的中位线 连接三角形两边中点的线段叫做三角形的中位线。 advantages, facing the Yangtze River Delta, Pearl River Delta, Shandong peninsula, Beijing-Tianjin-Tangshan area, targeted investment promotion several times. Industry-led unit and various town streets are developing detailed promotion p
21、lans, the basis of what is specific to each industry, has formed a kind of scale, need to bring in the kind of projects each town street has the kind of resources, what location, focus on the development of the kind of industries. Four stroke technology and science. Determinants of technology is the
22、 Countys economic development through scientific and technological innovation, improve product value-added and improve economic competitiveness, is the inevitable way to achieve leapfrog development. Talent is the city center citys first resource, is the primary industry development, and revitalizat
23、ion of the social protection. So, in terms of skills: to catch . Competitive. Encouraging enterprises to actively undertake science and technology projects, strengthening research cooperation, using advanced technology to increase the added value of their products to ensure that introduction of tran
24、sforming scientific and technological achievements during the year . . New research enterprises . . Home, creating innovative platforms . . Generic classifier. In: first, we must strengthen the cultivation of talent, efforts to increase vocational education and training and meet the basic demand of
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