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Why cant you use AA or ASS properties to prove triangles congruent?
Onels
There is no AA congruence property. Two triangles with the same angles are similar, but need not be congruent. In other words, they are the same 'shape' but different sizes. For example, an equilateral triangle can be big or small, but all equilateral triangles have 60 degree angles.
Although it is often said that there is no ASS congruence theorem in geometry, this isn't quite true. For prescribed values of angle, side, side, there are at most two different "congruence classes" of triangles realizing these values. In other words, there are really only at most two different types of triangles with those given values: any other triangle with the same values is congruent to one of those two.
When you study trigonometry, you will learn something called the "Law of Sines." It will give you at most two possible values for the angle opposite the middle S in aSs (they are supplementary to each other.) Then the ASA congruence theorem can be applied.
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