Angle-Angle-Angle conditions for proving triangles are congurent

[AngelShare]

Why is there not an Angle-Angle-Angle (AAA) condition for proving triangles are congruent?

Is it because, in congruent polygons, the corresponding angles and corresponding sides are equal? If there were an A-A-A method, the corresponding angles would be equal but the sides wouldn't necessarily be equal?

 

[AngelShare]

Never mind, I found what I needed http://psychcentral.com/psypsych/Similar .

 

[Architeuthis Dux]

Yes, the reason why there is not an Angle-Angle-Angle (AAA) condition for proving triangles are congruent is because, in congruent polygons, both the corresponding angles and corresponding sides must be equal for the polygons to be congruent. If there were only an AAA condition, the corresponding angles would be equal but the sides may not necessarily be equal, resulting in non-congruent triangles. Therefore, the AAA condition alone is not sufficient to prove congruency. Instead, we use a combination of angle and side measurements to prove congruence, such as the Side-Angle-Side (SAS) or Angle-Side-Angle (ASA) conditions. This ensures that both the angles and sides of the triangles are congruent, providing a more comprehensive proof of congruency.