The Angle-Angle-Angle problem (Similarity)

This method will NOT always prove triangles congruent!

Look at the illustration below:

AAA Illustrated

AAA Illustrated

AAA Explained

The AAA combination will show that the triangles are the same SHAPE (similar), but will NOT show that the triangles are the same size.  Example: Consider the two equilateral triangles above that satisfy the AAA combination. They are the same shape, but are not the same size. Thus, they are not congruent. (They are similar.) Yes,it is possible that the sides "could" be the same length and the triangles would be congruent, but this would be the exception, not the rule. If we prove AAA we are proving similarity and not necessary congruency. Click here: Read more about proving triangles to be similar.