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1、中考数学总复习专题基础知识回顾四三角形一、单元知识网络：二、考试目标要求：1了解三角形有关概念（内角、外角、中线、高、角平分线），会画出任意三角形的角平分线、中线和高，了解三角形的稳定性.2探索并掌握三角形中位线的性质.3了解全等三角形的概念，探索并掌握两个三角形全等的条件.4了解等腰三角形的有关概念，探索并掌握等腰三角形的性质和一个三角形是等腰三角形的条件；了解等边三角形的概念并探索其性质.5了解直角三角形的概念，探索并掌握直角三角形的性质和一个三角形是直角三角形的条件.6体验勾股定理的探索过程，会运用勾股定理解决简单问题；会用勾股定理的逆定理判定直角三角形.三、知识考点梳理知识点一、三角形
2、的概念及其性质1三角形的概念由不在同一直线上的三条线段首尾顺次相接所组成的图形叫做三角形.2三角形的分类(1)按边分类：(2)按角分类：3三角形的内角和外角(1)三角形的内角和等于180.(2)三角形的任一个外角等于和它不相邻的两个内角之和；三角形的一个外角大于任何一个和它不相邻的内角.4三角形三边之间的关系三角形任意两边之和大于第三边，任意两边之差小于第三边.5三角形内角与对边对应关系在同一个三角形内，大边对大角，大角对大边；在同一三角形中，等边对等角，等角对等边.6三角形具有稳定性.知识点二、三角形的“四心”和中位线三角形中的四条特殊的线段是：高线、角平分线、中线、中位线.1内心：三角形角
3、平分线的交点，是三角形内切圆的圆心，它到各边的距离相等.文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1
4、Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9
5、A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1
6、Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9
7、A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1
8、Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9
9、A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K32外心：三角形三边垂直平分线的交点，是三角形外接圆的圆心，它到三个顶点的距离相等.3重心：三角形三条中线的交点，它到每个顶点的距离等于它到对边中点距离的2 倍.4垂心：三角形三条高线的交点.5三角形的中位线：连结三角形两边中点的线段是三角形的中位线.中位线定理：三角形的中位线平行于第三边且等于第三边的一
10、半.要点诠释：(1)三角形的内心、重心都在三角形的内部.(2)钝角三角形的垂心、外心都在三角形的外部.(3)直角三角形的垂心为直角顶点，外心为直角三角形斜边的中点.(4)锐角三角形的垂心、外心都在三角形的内部.知识点三、全等三角形1定义：能完全重合的两个三角形叫做全等三角形.2性质：(1)对应边相等(2)对应角相等(3)对应角的平分线、对应边的中线和高相等(4)周长、面积相等3判定：(1)边角边(SAS)(2)角边角(ASA)文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:
11、CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A
12、2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:
13、CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A
14、2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:
15、CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A
16、2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:
17、CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3(3)角角边(AAS)(4)边边边(SSS)(5)斜边直角边(HL)(适用于直角三角形)要点诠释：判定三角形全等至少必须有一组对应边相等.知识点四、等腰三角形1定义：有两条边相等的三角形叫做等腰三角形.2性质：(1)具有三角形的一切性质.(2)两底角相等(等边对等角)(3)顶角的平分线，底边中线，底边上的高互相重合(三线合一)(4)等边三角形的各角都相等，且都等于60.3判定：(1)如果一个三角形有两个角相等，那么这两个角所对的边也相等(等角对等边)；(2)三个角都相等的三角形是等边三角形；(3)有一个角为60的等腰三角形是
18、等边三角形.要点诠释：(1)腰、底、顶角、底角是等腰三角形特有的概念；(2)等边三角形是特殊的等腰三角形.知识点五、直角三角形1定义：有一个角是直角的三角形叫做直角三角形.2性质：(1)直角三角形中两锐角互余；(2)直角三角形中，30锐角所对的直角边等于斜边的一半.文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI
19、2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R
20、7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI
21、2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R
22、7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI
23、2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R
24、7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3(3)在直角三角形中，如果有一条直角边等于斜边的一半，那么这条直角边所对的锐角等于30.(4)
25、勾股定理：直角三角形中，两条直角边的平方和等于斜边的平方.(5)勾股定理逆定理：如果三角形的三边长a，b，c 满足 a2+b2=c2，那么这个三角形是直角三角形.(6)直角三角形中，斜边上的中线等于斜边的一半；(7)SRt ABC=ch=ab，其中 a、b为两直角边，c 为斜边，h 为斜边上的高.3判定：(1)两内角互余的三角形是直角三角形；(2)一条边上的中线等于该边的一半，则这条边所对的角是直角，则这个三角形是直角三角形.(3)如果三角形两边的平方和等于第三边的平方，则这个三角形是直角三角形，第三边为斜边.知识点六、线段垂直平分线和角平分线1线段垂直平分线：经过线段的中点并且垂直这条线段的
26、直线，叫做这条线段的垂直平分线.线段垂直平分线的定理：(1)线段垂直平分线上的点与这条线段两个端点的距离相等.(2)与一条线段两个端点距离相等的点，在这条线段的垂直平分线上.线段垂直平分线可以看作是与线段两个端点距离相等的所有点的集合.2角平分线的性质：(1)角的平分线上的点到角的两边的距离相等；(2)到角的两边的距离相等的点在角的平分线上；(3)角的平分线可以看做是到角的两边距离相等的所有点的集合.四、规律方法指导1数形结合思想本单元中所学的三角形性质、角平分线性质、全等三角形的性质、直角三角形中的勾股定理等，都是在结合图形的基础上，求线段或角的度数，证明线段或角相等.在几何学习中，应会利用
27、几何图形解决实际问题.文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N
28、4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7
29、ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N
30、4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7
31、ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N
32、4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7
33、ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K32分类讨论思想在没给图形的前提下，画三角形或三角形一边上的高、三角形的垂心、外心时要考虑分类：三种情况，锐角三角形、直角三角形、钝角三角形.3.化归与转化思想在解决利用三角形的基础知识计算、证明问题时，通过做辅助线、利用所学知识进行准确推理等转化手段，归结为另一个相对较容易解决的或者已经有解决模式的问题，已知与未知之间的转化；数与形的转
34、化；一般与特殊的转化.4注意观察、分析、总结应将三角形的判定及性质作为重点，对于特殊三角形的判定及性质要记住并能灵活运用，注重积累解题思路和运用数学思想和方法解决问题的能力和培养，淡化纯粹的几何证明.学会演绎推理的方法，提高逻辑推理能力和逻辑表达能力，掌握几何证明中的分析，综合，转化等数学思想.经典例题透析考点一、三角形的概念及其性质1（1）（2010 山东济宁）若一个三角形三个内角度数的比为23 4，那么这个三角形是（）A.直角三角形B.锐角三角形C.钝角三角形 D.等边三角形思路点拨：三角形的内角和为180，三个内角度数的份数和是9，每一份度数是20，则三个内角度数分别为40、60、80，
35、是锐角三角形.答案：B（2）三角形的三边分别为3，1-2a，8，则 a 的取值范围是()A-6a-3 B -5 a-2 C2a5 Da-5 或 a-2 思路点拨：涉及到三角形三边关系时，尽可能简化运算，注意运算的准确性.解析：根据三角形三边关系得：8-3 1-2a 8+3，解得-5 a-2，应选 B.举一反三：【变式 1】已知 a，b，c 为 ABC的三条边，化简得 _.思路点拨：本题利用三角形三边关系，使问题代数化，从而化简得出结论.文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3
36、文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3
37、I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3
38、文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3
39、I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3
40、文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3
41、I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3
42、文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3解析：a，b，c 为 ABC的三条边a-b-c 0，b-a-c0=(b+c-a)+(a+c-b)=2c.【变式2】有五根细木棒，长度分别为1cm，3cm，5cm，7cm，9cm，现任取其中的三根木棒，组成一个三角形，问有几种可能()A.1 种 B.2 种 C.3 种 D.4 种解析：只有3、5、7 或 3、7、9或 5、7、9 三种.应选 C.【变式 3】等腰三角形中两条边长分别为3、4，则三角形的周长是_.思路点拨：要分类讨论，给出的边长中，可能分别是腰或底.注意满足三角形三边关系.解析：(1)当腰为 3 时，周
43、长=3+3+4=10；(2)当腰为 4 时，周长=3+4+4=11.所以答案为10 或 11.2（1）（2010 宁波市）如图，在ABC 中，AB AC，A 36，BD、CE 分别是 ABC、BCD的角平分线，则图中的等腰三角形有（）A5个B4 个 C3 个 D2 个考点：等腰三角形答案：A（2）如图在 ABC中，ABC=90，A=50，BD AC，则 CBD的度数是 _.考点：直角三角形两锐角互余.解析：ABC 中，C=ABC-A=90-50=40又 BD AC，CBD=C=40 .3已知 ABC的三个内角 A、B、C满足关系式B+C=3A，则此三角形中()A.一定有一个内角为45B.一定有
44、一个内角为60C.一定是直角三角形 D.一定是钝角三角形考点：三角形内角和180.文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX
45、3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K
46、3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX
47、3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K
48、3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX
49、3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K
50、3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3文档编码:CI2N4Y9A3S1 HX3I8C5A2R7 ZN1Y3N6H3K3思路点拨：会灵活运和三角形内角和等于180这一定理，即B+C=180-A.解析：ABC中，A+B+C=180，B+C=180-A B+C=3A，180-A=3A，A=45，选A，其它三个答案不能确定.举一反三：【变式 1】下图能说明1 2 的是()考点：三角形外角性质.思路点拨