今天为大家带来的是全等三角形的知识点总结。全等三角形作为平面几何的基础，是我们对理解几何图形必不可少的知识点，也是考试中非常重要的考点。下面就由我来帮助大家总结证明全等三角形的方法：

首先，在尝试证明两个三角形全等之前，我们必须先弄懂命题的概念，这是数学证明中最重要的逻辑。

1、判断正确或错误的句⼦叫做命题.正确的命题称为真命题，错误的命题称为假命题.

2、命题是由题设、结论两部分组成的.题设是已知事项;结论是由已知事项推出的事项.常可写成如果，那么的形式.⽤如果

开始的部分就是题设，⽽⽤那么开始的部分就是结论.

First, before trying to prove that two triangles are congruent, we must first understand the concept of proposition, which is the most important logic in mathematical proof.

1. A sentence that judges right or wrong is called a proposition. A correct proposition is called a true proposition, and a wrong proposition is called a false proposition.

2. The proposition is composed of two parts: the title and the conclusion. The title is the known matter; the conclusion is the matter derived from the known matter. It can often be written in the form of if and then. Use if

The beginning part is the proposition, and the beginning part is the conclusion.

3、⼀般来说，在两个命题中，如果第⼀个命题的题设是第⼆个命题的结论，⽽第⼀个命题的结论是第⼆个命题的题设，

那么这两个命题叫做互逆命题.如果把其中⼀个命题叫做原命题，那么另⼀命题就叫做它的逆命题.

4、如果⼀个定理的逆命题也是定理，那么这两个定理叫做互逆定理，其中的'⼀个定理叫做另⼀个定理的逆定理

3. Generally speaking, in two propositions, if the hypothesis of the first proposition is the conclusion of the second proposition, and the conclusion of the first proposition is the hypothesis of the second proposition,

Then these two propositions are called reciprocal propositions. If one of the propositions is called the original proposition, then the other proposition is called its inverse proposition.

4. If the inverse proposition of a theorem is also a theorem, then these two theorems are called reciprocal theorems, and one of them is called the inverse theorem of the other theorem.

其次，我们需要复习一些来自与三角形的知识，比如直角三角形的特点：

5、直⾓三⾓形的两个锐⾓互余.

5. The two acute angles of a right triangle are complementary to each other.

在搞清楚直角三角形的性质以及命题的判定之后，我们就可以尝试进行全等三角形的判定了，具体方法如下：

6、三⾓形全等的判定：(图中为需要证明全等三角形的常见形态)Judgment of congruence of triangles: (The picture shows the common forms of congruent triangles that need to be proved)

⽅法1：如果两个三⾓形有两边及其夹⾓分别对应相等，那么这两个三⾓形全等.简记为S.A.S.(或边⾓边).

⽅法2：如果两个三⾓形有两个⾓及其夹边分别对应相等，那么这两个三⾓形全等.简记为A.S.A.(或⾓边⾓)

⽅法3：如果两个三⾓形有两个⾓和其中⼀个⾓的对边分别对应相等，那么这两个三⾓形全等.简记为A.A.S.(或⾓⾓边).

⽅法4：如果两个三⾓形的三条边分别对应相等，那么这两个三⾓形全等.简记为S.S.S(或边边边).

⽅法5(只能⽤于直⾓三⾓形)：如果两个直⾓三⾓形的斜边和⼀条直⾓边分别对应相等，那么这两个直⾓三⾓形全等.简记

为H.L.(或斜边、直⾓边)

Method 1: If two triangles have two sides and their clips are correspondingly equal, then the two triangles are congruent. This method is abbreviated as S.A.S.

Method 2: If two triangles have two corners and their sides are correspondingly equal, then the two triangles are congruent. This method is abbreviated as A.S.A.

Method 3: If two triangles have two corners and the opposite sides of one of them are correspondingly equal, then the two triangles are congruent. This method is abbreviated as A.A.S..

Method 4: If the three sides of two triangles are correspondingly equal, then the two triangles are congruent. This method is abbreviated as S.S.S

Method 5 (only applicable to right triangles): If the hypotenuse and one right side of two right triangles are correspondingly equal, then the two right triangles are congruent. This method is abbreviated as H.L.