The property that is always true for a parallelogram is:
Diagonals bisect each other.
In a parallelogram, the two diagonals intersect at a point that divides each diagonal into two equal parts. The other properties listed (diagonals being perpendicular, diagonals being congruent, and diagonals bisecting opposite angles) are not true for all parallelograms; they may hold for specific types of parallelograms like rectangles and rhombuses, but not for parallelograms in general.