Question

What is proving triangles congruent by ASA and AAS

Answer 1

Triangles can be proved congruent by ASA and AAS, where ASA requires two angles and the included side to be equal, and AAS needs two angles and a non-included side to be congruent.

Step-by-step explanation:

Triangle congruence by ASA (Angle-Side-Angle) and AAS (Angle-Angle-Side) are two methods used in geometry to prove that two triangles are congruent, meaning they have the same size and shape. The ASA postulate states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent. To use the ASA postulate, you need to have two angles and the side between them (the included side) known to be equal in both triangles.

The AAS theorem says that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent. Here, the order is important: the side must not be between the two angles you are using to compare the triangles.

For example, consider two triangles, ΔABC and ΔDEF. If ∠A = ∠D, ∠B = ∠E, and side AB is equal to side DE (ASA), or side AC is equal to side DF (AAS), then ΔABC is congruent to ΔDEF.

Answer 2

So ASA is angle side angle, and that means that if you prove that the side, and the side adjacent to that side and the angle between those two sides are all congruent to another triangle's sides and angle, the triangles are both congruent.
The AAS is angle angle side, or something, so say you have a triangle and you prove that two of its angles are congruent along with a side to another triangle's, then it's AAS. I understand where the confusion might be. I guess it's just a matter of what you state first in your proof?