Given:
The diagonals of the parallelogram are perpendicular and are not congruent.
We have to determine what the parallelogram is ?
Now, if the diagonals are perpendicular,the parallelogram can be a rectangle, rhombus or a square.
If the diagonals are congruent then the parallelogram can be a square or rectangle.
But since the diagonals are not congruent means they are not equal so the parallelogram will be a rhombus.
Hence, the parallelogram is a rhombus.