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a rhombus
Not for every parallelogram. Only for a rhombus (diamond) or square will the diagonals bisect the opposite angles they connect, and diagonals are perpendicular. In rectangles, the diagonals do not bisect the angles and are notperpendicular, but they do bisect each other.
A quadrilateral whose diagonals bisect each other at right angles is a rhombus. each other at right angles at M. So AB = AD and by the first test above ABCD is a rhombus. 'If the diagonals of a parallelogram are perpendicular, then it is a rhombus
A rhombus is a parallelogram with all 4 sides congruent. The diagonals bisect(split in have) the interior angles. The diagonals are perpendicular to each other.
You need more information: the length of a side. Then, since the diagonals bisect one another at right angles, you can use Pythagoras's theorem to calculate their lengths.