After flipping and translating, two triangles that can completely coincide are called congruent triangles. Three sides and three angles of two triangles are equal. Congruent triangles refers to two congruent triangles whose three sides and three angles are equal.

The judgment theorem of triangle congruence 1, a triangle with three equilateral sides is congruent triangles. side by side

2. A triangle with two equal corners is congruent triangles. Corner edge

3. Two angles and their sides correspond to the congruence of a triangle. ASA (corner)

4. The opposite sides of two angles and one angle correspond to congruences of equal triangles. Corner edge

5. In a pair of right-angled triangles, the hypotenuse is equal to the other right-angled side. Right angle, hypotenuse, edge

Congruent triangles, the nature should be clarified. The corresponding edges are equal and the corresponding angles are the same. The four theorems of angle, angle, edge, edge, angle and edge should be completely remembered.

Congruent triangles's judgment AAA (Angle, Angle, Angle) cannot be verified, that is to say, any three angles of two triangles correspond to the same. But this can't judge congruent triangles, AAA can judge similar triangles. In geometry, two straight lines overlap to form a point and an angle. Moreover, if the line is infinitely long or infinitely enlarged, the angle will not change. Similarly, in the left picture, the two triangles are similar, and the relationship between the two triangles is enlarged and narrowed, so the angle will not change.

In this way, we can know that if the edge is stretched infinitely in proportion, the angle will remain the same. So AAA can't judge congruent triangles.

However, in spherical geometry, AAA can judge congruent triangles (proved by the angular relationship between a triangle and its polar symmetrical triangle), while AAS cannot judge congruent triangles (the sum of the internal angles of a spherical triangle is greater than 180).