If you can show the size of a leg (and there for all corresponding legs) or the area is different in the two triangles they are similar NOT congruent. So, just because the angles are the same ... for example an equilateral triangle... if the triangles are not the same size they are not congruent. So, all one side needs to prove is that the two triangles with identical angles have different areas or size legs, then they prove their case.
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