Two triangles that can completely overlap are called congruent triangles, and "congruence" is represented by the symbol "",which is pronounced "congruence".

When two triangles completely overlap, the overlapping vertices are called corresponding vertices, the overlapping edges are called corresponding edges, and the overlapping angles are called corresponding angles.

It can be concluded that the corresponding edges of congruent triangles are equal and the corresponding angles are equal.

Proof: There are three kinds.

1. Three groups of corresponding edges are equal (sss for short).

2. There is an angle that is congruent with two triangles that sandwich the two sides of the angle.

3. Two triangles have two angles and their sides correspond to each other (asa)

Note: S is the abbreviation of edge and A is the abbreviation of angle.

Push from 3 o'clock

4. Two triangles have two angles, and the opposite sides of one angle correspond to each other.

These can prove that:

The distance between the point on the perpendicular of the line segment and the two endpoints of the line segment is equal.

The point on the bisector of an angle is equal to the distance on both sides of the angle.

There is another way to judge.

A right triangle is unique:

The hypotenuse and the right-angled side correspond to the congruence (hl) of two equal right-angled triangles.

Congruent triangles definition

1、

Conceptual understanding:

When two triangles have the same shape, size and symmetry, one of them can be translated, rotated and symmetrical to make it coincide with the other. These two triangles are called congruent triangles, and the judgment of their congruence is a powerful tool for geometric proof.

2, triangle congruence judgment axiom and inference is:

(1) "corner" is abbreviated as "sas"

② The abbreviation of "corner" is "asa"

(3) "Edge" is abbreviated as "sss"

(4) The abbreviation of "corner edge" is "aas"

Note: In congruence judgment, there are no aaa and ssa, and neither of them can uniquely determine the shape of a triangle.

3、

The essence of congruent triangles;

The corresponding angles and sides of congruent triangles are equal.

note:

1) is a condition, and the conclusion is that the corresponding angle and the corresponding edge are equal.

But the judgment of congruence is just the opposite.

2) It is the key to learn to find out the corresponding edges and angles in two congruent triangles accurately by using nature and judgment. When writing the congruence of two triangles, the corresponding vertices, angles and edges must be written in the same order, which provides convenience for finding the corresponding edges and angles.