The correct answer is congruent

If the area of two similar triangles is equal, then it does not necessarily mean that they are congruent or equilateral. The correct answer is (C) congruent.

Similar triangles are triangles that have the same shape but not necessarily the same size. They have the same angles but different side lengths. The ratio of the corresponding sides of similar triangles is always constant, and this ratio is called the scale factor.

If two triangles are similar and their areas are equal, it means that the squares of the corresponding sides of the triangles are in the same ratio. Since the area of a triangle is proportional to the square of its side length, two triangles with equal areas must have their corresponding sides in the same ratio.

Therefore, if two similar triangles have equal areas, then their corresponding sides are also equal in length. This implies that the triangles are congruent, meaning that they have the same shape and size. Therefore, the correct answer is (C) congruent.

In summary, if the area of two similar triangles is equal, it means that the triangles are congruent, not necessarily equilateral or isosceles.