(完整word版)八年级数学知识点总结汇总(下)新人教版(良心出品必属精品).pdf
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1、1 八年级数学知识点总结汇总(下)二次根式【知识回顾】1.二次根式:式子a(a0)叫做二次根式。2.最简二次根式:必须同时满足下列条件:被开方数中不含开方开的尽的因数或因式;被开方数中不含分母;分母中不含根式。3.同类二次根式:二次根式化成最简二次根式后,若被开方数相同,则这几个二次根式就是同类二次根式。4.二次根式的性质:(1)(a)2=a(a0);(2)aa25.二次根式的运算:(1)因式的外移和内移:如果被开方数中有的因式能够开得尽方,那么,就可以用它的算术根代替而移到根号外面;如果被开方数是代数和的形式,那么先解因式,?变形为积的形式,再移因式到根号外面,反之也可以将根号外面的正因式平
2、方后移到根号里面(2)二次根式的加减法:先把二次根式化成最简二次根式再合并同类二次根式(3)二次根式的乘除法:二次根式相乘(除),将被开方数相乘(除),所得的积(商)仍作积(商)的被开方数并将运算结果化为最简二次根式ab=ab(a0,b0);bbaa(b0,a0)(4)有理数的加法交换律、结合律,乘法交换律及结合律,?乘法对加法的分配律以及多项式的乘法公式,都适用于二次根式的运算【典型例题】1、概念与性质例 1 下列各式 1)22211,2)5,3)2,4)4,5)(),6)1,7)2153xaaa,a(a0)a(a0)0(a=0);精品资料-欢迎下载-欢迎下载 名师归纳-第 1 页,共 19
3、 页 -2 其中是二次根式的是 _(填序号)例 2、求下列二次根式中字母的取值范围(1)xx315;(2)22)-(x例 3、在根式 1)222;2);3);4)275xabxxyabc,最简二次根式是()A1)2)B3)4)C1)3)D1)4)例 4、已知:的值。求代数式22,211881xyyxxyyxxxy例 5、(2009 龙岩)已知数 a,b,若2()ab=ba,则()A.ab B.a0,b0时,则:1aabb;1aabb例 8、比较53与23的大小。5、规律性问题例 1.观察下列各式及其验证过程:,验证:;验证:.精品资料-欢迎下载-欢迎下载 名师归纳-第 3 页,共 19 页 -
4、文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:C
5、L5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4
6、Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8
7、HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P
8、6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4
9、ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10
10、B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P94(1)按照上述两个等式及其验证过程的基本思路,猜想4415的变形结果,并进行验证;(2)针对上述各式反映的规律,写出用n(n2,且 n 是整数)表示的等式,并给出验证
11、过程.精品资料-欢迎下载-欢迎下载 名师归纳-第 4 页,共 19 页 -文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F
12、4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8
13、 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9
14、P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4
15、 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J1
16、0B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P
17、9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P95 勾股定理1.勾股定理:如果直角三角形的两直角边长分别为a,b,斜边长为 c,那么 a2b2
18、=c2。2.勾股定理逆定理:如果三角形三边长a,b,c 满足 a2b2=c2。,那么这个三角形是直角三角形。3.经过证明被确认正确的命题叫做定理。我们把题设、结论正好相反的两个命题叫做互逆命题。如果把其中一个叫做原命题,那么另一个叫做它的逆命题。(例:勾股定理与勾股定理逆定理)4.直角三角形的性质(1)、直角三角形的两个锐角互余。可表示如下:C=90 A+B=90(2)、在直角三角形中,30角所对的直角边等于斜边的一半。A=30可表示如下:BC=21AB C=90(3)、直角三角形斜边上的中线等于斜边的一半ACB=90 可表示如下:CD=21AB=BD=AD D为 AB的中点5、摄影定理在直角
19、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ACB=90 BDADCD2ABADAC2CD AB ABBDBC26、常用关系式由三角形面积公式可得:AB CD=ACBC 7、直角三角形的判定 1、有一个角是直角的三角形是直角三角形。2、如果三角形一边上的中线等于这边的一半,那么这个三角形是直角三角形。3、勾股定理的逆定理:如果三角形的三边长a,b,c 有关系222cba,那么这个三角形是直角三角形。8、命题、定理、证明1、命题的概念判断一件事情的语句,叫做命题。理解:命题的定义包括两层含义:(1)命题必须是个完整的句子;(2)这个句子
20、必须对某件事情做出判断。2、命题的分类(按正确、错误与否分)精品资料-欢迎下载-欢迎下载 名师归纳-第 5 页,共 19 页 -文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R
21、2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH
22、4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1
23、D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档
24、编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5
25、B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y10S8 HV6P9P6R2M4 ZH4J10B1D6P9文档编码:CL5B5F4Y1
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