SINCE there is SSS postulate,can we have AAA postulate and SSA postulate?
Answers
why ssa congruence is not possible
if we are given two sides and a non-included angle it is not enough to prove congruence. But there are two triangles possible that have the same values, so SSA is not sufficient to prove congruence.
In the first figure in the attachment, the two triangles above are initially congruent. But if you click on "Show other triangle" you will see that there is another triangle that is not congruent but that still satisfies the SSA condition. AB is the same length as PQ, BC is the same length as QR, and the angle A is the same measure as P. And yet the triangles are clearly not congruent - they have a different shape and size.
why aaa congruence is not possible
If all three angles in one triangle are the same as the corresponding angles in the other, then the triangles may always not be congruent. So for example, in the triangle in the second attachment, the interior angle ∠P is exactly equal to the corresponding angle ∠L in the other triangle. ∠Q is equal to ∠M, and ∠R is equal to ∠N. And so, even though all three corresponding angles are equal, the triangles are not congruent.
