Triangles $A B C$ and $X Y Z$ have the same area.
Which of these extra conditions, taken independently, would imply that they are congruent?
(1) $A B = X Y$ and $B C = Y Z$
(2) $A B = X Y$ and $\angle A B C = \angle X Y Z$
(3) $\angle A B C = \angle X Y Z$ and $\angle B C A = \angle Y Z X$