No. The diagonals of a parallelogram are congruent if and only if the parallelogram is a rectangle.
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Yes because a rhombus is like a parallelogram
square
No because the diagonals of a parallelogram are of different lengths
Opposite angles are congruent in a parallelogram.
They are sometime congruent because a square is a parallelogram and its sides are congruent and a rectangle is one and its sides aren't congruent.