Question

Why is AAA not congruent Theorem?

Answer 1

AAA congruence stands for Angle Angle Angle congruence.

This can determine whether 2 or more triangles are similar but not congruent.

This is because the corresponding angles of 2 or more triangles can be equal, but it can only be congruent if the sides are also equal.

A simple example. There are a variety of equilateral triangles out there, but do they look the same? No.

The triangles may be of different sizes which goes against congruence rules.

have a good day unlike

Answer 2

AAA refers to three congruent angles. The problem with is that just because a triangle’s corresponding angles are congruent, that doesn’t necessarily mean their sides are congruent as well. Recall the definition of an angle: the intersection of two rays at a point called the vertex. Rays have a starting point but have infinite distance, so elongating a ray does not change the angle measure; it stays the same. This is the case with segments or sides in a triangle as well. Essentially, a triangle may have three angle measures of 60,° but the side lengths of two triangles may not be congruent, since a longer segment will not affect the angle measure. So, for example, if two triangles have three congruent angles, there is no way to determine wether their side lengths are congruent. One triangle might have a side length of 5 and its corresponding side on the second triangle may be 10, so even though the angles are congruent, the sides may not be. Thus, the AAA Theorem is a similarity theorem.