2022年人教版九年级数学下册知识点总结资料 .pdf

1人教版九年级数学下册知识点总结第二十六章二次函数.1261 二次函数及其图像.1262 用函数观点看一元二次方程.6263 实际问题与二次函数.6第二十七章相似.6271 图形的相似.6272 相似三角形.7273 位似.8第二十八章锐角三角函数.8281 锐角三角函数.9282 解直角三角形.10第二十九章投影与视图.12291 投影.12292 三视图.12第二十六章二次函数261二次函数及其图像二次函数(quadratic function)是指未知数的最高次数为二次的多项式函数。二次函数可以表示为f(x)=ax+bx+c(a不为0)。其图像是一条主轴平行于y 轴的抛物线。般的，自变量x 和因变量y 之间存在如下关系：般式y=ax A 2;+bx+c（a 工0,a、b、c 为常数），顶点坐标为（-b/2a,-（4ac-b A 2)/4a)2顶点式y=a(x+m)A 2+k(a 工0,a、m k 为常数)或y=a(x-h)A2+k(a 工0,a、h、k为常数)，顶点坐标为(-m,k)对称轴为x=-m，顶点的位置特征和图像的开口方向与函数y=ax A2的图像相同，有时题目会指出让你用配方法把一般式化成顶点式；交点式y=a(x-x1)(x-x2)仅限于与x 轴有交点A(x1,0)和B(x2,0)的 抛物线;重要概念：a,b,c为常数，a0,且a决定函数的开口方向，a0时,开口方向向上，a0时，抛物线向上开口；当av0时，抛物线向下开口|a|越大，则抛物线的开口越小。决定对称轴位置的因素4.一次项系数b和二次项系数a共同决定对称轴的位置特别地，当b=0时，抛物线的对称轴是y轴（即直线x=0）文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T44当a与b同号时（即ab 0），对称轴在y轴左；因为若对称轴在左边则对称轴小于0，也就是-b/2a0,所以b/2a 要小于0，所以a、b 要异号可简单记忆为左同右异，即当a与b同号时（即ab 0）,对称轴在y轴左；当a 与b 异号时（即abv 0），对称轴在y 轴右。事实上，b 有其自身的几何意义：抛物线与y 轴的交点处的该抛物线切线的函数解析式（一次函数）的斜率k 的值。可通过对二次函数求导得到。决定抛物线与y 轴交点的因素5.常数项c 决定抛物线与y 轴交点。抛物线与y 轴交于（0，c）抛物线与x 轴交点个数6.抛物线与x 轴交点个数=bA2-4ac 0时，抛物线与x轴有2个交点。=bA2-4ac=0 时，抛物线与x轴有1个交点。=bA2-4ac v 0 时，抛物线与x 轴没有交点。X 的取值是虚数（x=-bVbA2-4ac的值的相反数，乘上虚数i，整个式子除以2a）当a0 时，函数在x=-b/2a 处取得最小值f（-b/2a）=4ac-b²/4a 在x|x-b/2a 上是增函数；抛物线的开口向上；函数的值域是y|y 4ac-bA2/4a相反不变当b=0 时，抛物线的对称轴是y 轴，这时，函数是偶函数，解析式变形为y=axA2+c（a 工0）特殊值的形式7.特殊值的形式文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T45当x=1时y=a+b+c 当x=-1 时y=a-b+c 当x=2 时y=4a+2b+c 当x=-2 时y=4a-2b+c 二次函数的性质8.定义域：R 值域：(对应解析式，且只讨论a 大于0 的情况，a 小于0 的情况请读者自行推断)(4ac-bA2)/4a,正无穷)：t，正无穷)奇偶性：当b=0时为偶函数，当b0时为非奇非偶函数。周期性：无解析式：y=axA2+bx+c 一般式 aM 0 a 0,则抛物线开口朝上；a v 0，则抛物线开口朝下；极值点：(-b/2a，(4ac-bA2)/4a)；厶=bA2-4ac,0，图象与x轴交于两点：(-b-VA/2a，0)和(卜b+VA/2a，0);二0，图象与x轴交于一点：(-b/2a，0)；Av 0，图象与x 轴无交点；y=a(x-hF2+k顶点式 此时，对应极值点为(h，k)，其中h=-b/2a，k=(4ac-bA2)/4a;y=a(x-x1)(x-x2)交点式(双根式)(aM 0)对称轴X=(X1+X2)/2 当a0且X(X1+X2)/2 时，丫随X的增大而增大，当a0 且X(X1+X2)/2 时Y 随X 的增大而减小此时，x1、x2即为函数与X轴的两个交点，将X、Y代入即可求出解析式(一般与一元二次方程连文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T46用)。交点式是Y=A(X-X1)(X-X2)知道两个x 轴交点和另一个点坐标设交点式。两交点X值就是相应X1 X2值。262用函数观点看一元二次方程1.如果抛物线y ax2 bx c 与x轴有公共点，公共点的横坐标是Xo，那么当x x0时，函数的值是0，因此 x x0就是方程 ax2 bx c 0 的一个根。2.二次函数的图象与x轴的位置关系有三种：没有公共点，有一个公共点，有两个公共点。这对应着一元二次方程根的三种情况：没有实数根，有两个相等的实数根，有两个不等的实数根。263实际问题与二次函数在日常生活、生产和科研中，求使材料最省、时间最少、效率最高等问题，有些可归结为求二次函数的最大值或最小值。第二十七章相似271 图形的相似概述如果两个图形形状相同,但大小不一定相等,那么这两个图形相似。(相 似的符号：S)判定如果两个多边形满足对应角相等，对应边的比相等，那么这两个多边形相似。相似比文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T47全等。性质相似多边形的对应角相等，对应边的比相等。相似多边形的周长比等于相似比。相似多边形的面积比等于相似比的平方。27.2相似三角形判定1.两个三角形的两个角对应相等2.两边对应成比例，且夹角相等3.三边对应成比例4.平行于三角形一边的直线和其他两边或两边延长线相交，所构成的三角形与原三角形相似。例题性质1.相似三角形的一切对应线段（对应高、对应中线、对应角平分线、外接圆半径、内切圆半径等）的比等于相似比。2.相似三角形周长的比等于相似比。3.相似三角形面积的比等于相似比的平方27.3位似如果两个图形不仅是相似图形，而且每组对应点的连线交于一点，对应边互相平行，那么这两个图形叫做位似图形，这个点叫做位似中心,这时的相似比又称为位似比。相似多边形的对应边的比叫相似比。相似比为1时，相似的两个图形vZ A=Z A;/B=Z B 文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T48性质位似图形的对应点和位似中心在同一直线上，它们到位似中心的距离之比等于相似比。位似多边形的对应边平行或共线。位似可以将一个图形放大或缩小。位似图形的中心可以在任意的一点，不过位似图形也会随着位似中心的位变而位变。根据一个位似中心可以作两个关于已知图形一定位似比的位似图形这两个图形分布在位似中心的两侧，并且关于位似中心对称。1、位似是一种具有位置关系的相似，所以两个图形是位似图形，必定是相似图形，而相似图形不一定是位似图形；2、两个位似图形的位似中心只有一个；3、两个位似图形可能位于位似中心的两侧，也可能位于位似中心的一侧；4、位似比就是相似比.利用位似图形的定义可判断两个图形是否位似;5、平行于三角形一边的直线和其它两边相交，所构成的三角形与原三角形位似。第二十八章锐角三角函数281锐角三角函数锐角角A的正弦(sin),余弦(cos)和正切(tan),余切(cot)以及正割(sec),(余割csc)都叫做角A的锐角三角函数。正弦(sin)等于对边比斜边，余弦(cos)等于邻边比斜边正切(tan)等于对边比邻边；余切(cot)等于邻边比对边正割(sec)等于斜边比邻边余割(csc)等于斜边比对边正切与余切互为倒数互余角的三角函数间的关系。sin(90 -a)=cos a,cos(90 -a)=sin a,文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T4文档编码:CM4P1N6A9Q5 HA5J4L6Z10R6 ZX8G8O6M9T49tan(90 -a)=cot a,cot(90 -a)=ta n a.同角三角函数间的关系平方关系：sinA2(a)+cosA2(