Is it possible that two triangles satisfy these conditions?

Question

Are there two triangles with equal angles and a pair of equal sides which are not congruent? If yes, please give an example.

Answer 1

For congruent triangle to exist, they must both share: SSS, SAS, ASA, AAS and HL. There for, on any two triangle with the same angles and a pair of equal sides, the "AAS" rule comes into play, and says, no, you cannot. Correct me if I'm wrong, but this is what I think.

Answer 2

Take a right triangle, draw the attitude from the right angle. You then have several pairs of examples.