Because "edges and corners" prove that triangle congruence is a false proposition, there are counterexamples, as follows:

The two triangles at the corners are not necessarily congruent, as shown in the following figure:

In mathematics, congruence generally refers to congruent triangles. Congruent triangles refers to two triangles with the same shape. Congruent triangles's corresponding angles and sides are equal.

Extended data:

There are five ways to prove congruent triangles.

1, SSS (side by side)

That is, three sides correspond to the congruence of two equal triangles.

2. Corner edge

That is, the two sides of a triangle are equal, and the included angle between the two sides also corresponds to the congruence of two equal triangles.

3.ASA (corner corner)

That is, the two angles of a triangle are equal, and the two angles are congruent with two equal triangles.

4. Corner edge

That is, the two angles of a triangle are equal, and the corresponding sides of the two angles are equal to the two triangles.

5.HL (right angle hypotenuse)

That is to say, the hypotenuse and right-angled side in a right triangle correspond to the congruence of two right-angled triangles.