八年级上册数学知识点总结1

八年级数学知识点总结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)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 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 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 County's 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 city's first 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 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 increase 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 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 University 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.AD?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. 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 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. Four stroke technology and science. Determinants of technology is the County's 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 city's first 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 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 increase 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 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 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)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 三角形的两边之和大于第三边的性质历年来是经常考到的填空的类型，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 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. Four stroke technology and science. Determinants of technology is the County's 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 city's first 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 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 increase 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 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 University to find experts3 (1)三角形共有三条中位线，并且它们又重新构成一个新的三角形。 (2)要会区别三角形中线与中位线。 三角形中位线定理:三角形的中位线平行于第三边，并且等于它的一半。 三角形中位线定理的作用: 位置关系:可以证明两条直线平行。 数量关系:可以证明线段的倍分关系。 常用结论:任一个三角形都有三条中位线，由此有: 结论1:三条中位线组成一个三角形，其周长为原三角形周长的一半。 结论2:三条中位线将原三角形分割成四个全等的三角形。 结论3:三条中位线将原三角形划分出三个面积相等的平行四边形。 结论4:三角形一条中线和与它相交的中位线互相平分。 结论5:三角形中任意两条中位线的夹角与这夹角所对的三角形的顶角相等。 4、直角三角形的性质 (1)直角三角形的两个锐角互余 (2)在直角三角形中，30?角所对的直角边等于斜边的一半。 (3)直角三角形斜边上的中线等于斜边的一半 )勾股定理:直角三角形两直角边a，b的平方和等于斜边c的平(4 222a，b,c方，即 (5)摄影定理 在直角三角形中，斜边上的高线是两直角边在斜边上的摄影的比例中项，每条直角边是它们在斜边上的摄影和斜边的比例中项 2?ACB=90? CD,AD,BD 2 ,AC,AD,AB 2CD?AB BC,BD,AB (6)常用关系式 ,,由三角形面积公式可得:ABCD=ACBC 中考规律盘点及预测 特殊三角形中的等腰三角形与第一章的全等三角形的证明结合起来这种题型会常出现，等腰三角形的性质是基础知识，必须得掌握并灵活的运用到各类题型中去，这类题型中考也是必考的。 第三章 一元一次不等式 复习总目 1、 理解不等式的三个基本性质 2、 会用不等式的基本性质解一元一次不等式并掌握不等式的解题步骤 3、会解由两个一元一次不等式组成的不等式组 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 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. Four stroke technology and science. Determinants of technology is the County's 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 city's first 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 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 increase 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 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 University to find experts 知识点概要 一、不等式的概念 1、不等式:用不等号表示不等关系的式子，叫做不等式。 2、不等式的解集:对于一个含有未知数的不等式，任何一个适合这个不等式的未知数的值，都叫做这个不等式的解。 3、对于一个含有未知数的不等式，它的所有解的集合叫做这个不等式的解的集合，简称这个不等式的解集。 4、求不等式的解集的过程，叫做解不等式。 5、用数轴表示不等式的方法 二、不等式基本性质 1、不等式两边都加上(或减去)同一个数或同一个整式，不等号的方向不变。 2、不等式两边都乘以(或除以)同一个正数，不等号的方向不变。 3、不等式两边都乘以(或除以)同一个负数，不等号的方向改变。 4、说明:?在一元一次不等式中，不像等式那样，等号是不变的，是随着加或乘的运算改变。?如果不等式乘以0，那么不等号改为等号所以在题目中，出乘以的数，那么就要看看题中是否出现一元一次不等式，如果出现了，那么不等式乘以的数就不等为0，否则不等式不成立; 三、一元一次不等式 1、一元一次不等式的概念:一般地，不等式中只含有一个未知数，未知数的次数是1， 且不等式的两边都是整式，这样的不等式叫做一元一次不等式。 2、解一元一次不等式的一般步骤:(1)去分母(2)去括号(3)移项(4)合并同类项(5)将x项的系数化为1 四、一元一次不等式组 1、一元一次不等式组的概念:几个一元一次不等式合在一起，就组成了一个一元一次不等式组。 2、几个一元一次不等式的解集的公共部分，叫做它们所组成的一元一次不等式组的解集。 3、求不等式组的解集的过程，叫做解不等式组。 4、当任何数x都不能使不等式同时成立，我们就说这个不等式组无解或其解为空集。 5、一元一次不等式组的解法 (1)分别求出不等式组中各个不等式的解集 (2)利用数轴求出这些不等式的解集的公共部分，即这个不等式组的解集。 6、不等式与不等式组 不等式:?用符号〉，=，〈号连接的式子叫不等式。?不等式的两边都加上或减去 同一个整式，不等号的方向不变。?不等式的两边都乘以或者除以一个正数，不等 号方向不变。?不等式的两边都乘以或除以同一个负数，不等号方向相反。 7、不等式的解集: 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 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. Four stroke technology and science. Determinants of technology is the County's 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 city's first 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 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 increase 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 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 University to find experts5 ?能使不等式成立的未知数的值，叫做不等式的解。 ?一个含有未知数的不等式的所有解，组成这个不等式的解集。 ?求不等式解集的过程叫做解不等式 中考规律盘点及预测 一元一次不等式(组)的解法及其应用，在初中代数中有比较重要的地位，它是继一元一次方程、二元一次方程的学习之后，又一次数学建模思想的学习，是培养学生问题和解决问题能力的重要，在近几年来的考试中会出现此类型的题目 第四章 图形与坐标 复习总目 1、掌握平面直角坐标系的建立和坐标点的描述 2、根据需要建立适当的直角坐标系，并在直角坐标系中画出图形 3、掌握坐标平面内的图形的轴对称和平移的变换 知识点概要 1、平面上物体的位置可以用有序实数对来确定。 2、在平面内确定物体的位置一般需要几个数据?有哪些方法? (1)用有序数对来确定; (2)用方向和距离(方位)来确定; 3、在平面内有公共原点而且互相垂直的两条数轴，就构成了平面直角坐标系。简称直角坐标系,坐标系所在的平面就叫做坐标平面 4、掌握各象限上及x轴，y轴上点的坐标的 特点: 第一象限(+，+);第二象限(,，+);第三象限(,，,);第四象限(+，,) 5、x轴上的点纵坐标为0，表示为(x，0);y轴上的点横坐标为0，表示为(0，y) 6、(1)关于x轴对称的两点:横坐标相同，纵坐标互为相反数。 (2)关于y轴对称的两点:纵坐标相同，横坐标互为相反数。 (3)关于原点对称的两点:横坐标互为相反数，纵坐标互为相反数。 7、平移 点a(x1,y1)向右、左平移 h个单位，则得到的新坐标a’(x1+/-h,y1) 点b(x2,y2)向上、下平移 g个单位，则得到的新坐标a’(x2,y2+/-g) 中考规律盘点及预测 通过对近几年各地的中考试题的研究发现，对有关图形的轴对称、平移、旋转、相似、图形与坐标等知识点的考查呈发展趋势，题型以选择、填空、作图、解答等多面孔出现。 第五章 一次函数 复习总目 1、能用待定系数法求一次函数的解析式 2、会根据一次函数的图象解相应的问题并会取得函数解析式的基本方法和步骤 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 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. Four stroke technology and science. Determinants of technology is the County's 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 city's first 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 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 increase 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 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 University to find experts 3、掌握一次函数的性质 知识点概要 1、一次函数:形如y=kx+b (k?0, k, b为常数)的函数。 注意:(1)k?0,否则自变量x的最高次项的系数不为1; (2)当b=0时，y=kx，y叫x的正比例函数。 2、图象:一次函数的图象是一条直线， (1)两个常有的特殊点:与y轴交于(0，b);与x轴交于(-，0) (2)由图象可以知道，直线y=kx+b与直线y=kx平行，例如直线:y=2x+3与直线y=2x-5 都与直线y=2x平行。 3、性质: (1)图象的位置: (2)增减性 k>0时，y随x增大而增大 k<0时，y随x增大而减小 4(求一次函数解析式的方法 求函数解析式的方法主要有三种 (1)由已知函数推导或推证 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 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. Four stroke technology and science. Determinants of technology is the County's 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 city's first 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 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 increase 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 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 University to find experts7 (2)由实际问题列出二元方程，再转化为函数解析式，此类题一般在没有写出函数解析式前无法(或不易)判断两个变量之间具有什么样的函数关系。 (3)用待定系数法求函数解析式。 “待定系数法”的基本思想就是方程思想，就是把具有某种确定形式的数学问题，通过引入一些待定的系数，转化为方程(组)来解决，题目的已知恒等式中含有几个等待确定的系数，一般就需列出几个含有待定系数的方程，本单元构造方程一般有下列几种情况: ?利用一次函数的定义 构造方程组。 ?利用一次函数y=kx+b中常数项b恰为函数图象与y轴交点的纵坐标，即由b来定点;直线y=kx+b平行于y=kx，即由k来定方向 。 ?利用函数图象上的点的横、纵坐标满足此函数解析式构造方程。 ?利用题目已知条件直接构造方程 。 中考规律盘点与预测 通过对近几年各地的中考试题的研究发现，对关于一次函数往往与反比例函数结合起来出现在选择题中，与三角形结合出现在计算题中。 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 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. Four stroke technology and science. Determinants of technology is the County's 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 city's first 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 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 increase 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 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 University to find experts