They become the diagonals of a parallelogram.
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A rhombus
No not normally only if the parallelogram is in the form of a rectangle will it then have congruent diagonals.
The best classification for a parallelogram that has perpendicular diagonals is a rhombus. A rhombus has four sides that are congruent. The also diagonals bisect the vertex angles of this type of parallelogram.
Yes because a rhombus is like a parallelogram
A rhombus, square, kite or arrowhead.