Congruent triangles refers to a triangle whose two sides and angles are exactly equal.

In mathematics, when two triangles are put together, it is found that the length and included angle of each side of the two triangles are exactly the same, then the two triangles are congruent triangles. The nature, proof method and application of congruent triangles will be introduced in detail below.

Congruent triangles has many properties, one of which is that their trilateral metric and triangular metric are equal, that is, for two congruent triangles, their corresponding edges and corresponding angles are completely equal. In addition, congruent triangles also has an important reflexive property, that is, if three sides of two triangles and triangle metrics are equal, then the two triangles are congruent triangles.

There are many ways to prove that two triangles are congruent, among which SAS method is the most commonly used, that is, it is known that two angles are equal, the side length between two angles and so on. In addition, there are SSS method, ASA method, AAS method and HL method, each of which has its own applicable scene and scope, and needs to be selected according to the specific situation.

Congruent triangles is widely used in geometry. For example, we can use the properties of congruent triangles to find out the distances and angles that are difficult to measure. In addition, congruent triangles can also be used to solve complex geometric problems, such as sine theorem and cosine theorem.

Congruent triangles is one of the most basic concepts in geometry. It has a strong nature of proof and wide application value, and is of great significance to mathematics learning and solving practical problems.

In addition, congruent triangles has some other important properties and theorems. For example, the height, midline, inscribed circle and circumscribed circle of congruent triangles are all equal, which provides convenience for solving some complicated triangle problems. In addition, congruent triangles also satisfies the properties of folding, shearing, symmetry and angular bisector theorem.

In the process of proving congruent triangles, we need to pay attention to some details. For example, when using SAS method, it is necessary to ensure that the side length between two corners is a * * * plane line segment, otherwise the congruent triangles cannot be constructed. When using ASA method to prove congruent triangles, we should pay attention to know whether two angles and the side length between them can uniquely determine a triangle. If not, it can't be proved by ASA method.

In mathematics learning and practical application, congruent triangles is a very basic but very important concept. Mastering congruent triangles's properties, theorems and proof methods can lay a solid foundation for us to solve geometric problems better. At the same time, congruent triangles is an indispensable theoretical tool for related occupations, such as construction engineers and surveyors.