Question

The five triangle congruence are sss, sas, aas, asa and hl criteria. Fully explain why aaa is not a triangle congruence criteria

Answer 1

As you may know, the addition of all the interior angles of a triangle always adds up to 180°.

So if we know two angles of the triangle, A1, and A2, we can find the third angle as:

A1 + A2 + X = 180°

X = 180° - A1 - A2.

Se with only knowing two angles, we can find the third angle.

So aaa is a criteria equivalent to aa.

Now, the problem with this criteria is that also works for finding similar triangles (for example, an equilateral triangle of sides 10 and an equilateral triangle of sides 20 are similar, as the angles are the same, but are not congruent, as the length of the sides is different) and this happens because we only have information of the angles and know nothing of the sides.