Triangles $ABC$ and $XYZ$ have the same area.

Which of these extra conditions, taken independently, would imply that they are congruent?

(1) $AB=XY$ and $BC=YZ$

(2) $AB=XY$ and $\angle ABC=\angle XYZ$

(3) $\angle ABC=\angle XYZ$ and $\angle BCA=\angle YZX$