By the semiperimeter formula, given the area and two sides, the third side can be calculated, so area and two sides is sufficient to prove triangles congruent. If two pairs of angles are congruent, the third pair must be congruent. With all the angles known, the law of sines can give the ratio of the sides and be used to express all sides in terms of one of them. Then that and the area can be used in the semiperimeter formula to solve for one side, which can solve for the other two. Are area, one side, and one angle sufficient to prove congruence? Phrased another way, can you make two triangles with an area of x, one pair of congruent sides of length y, and one pair of congruent angles with measure z that are not congruent? If it is possible, can you give an example?