a rhombus
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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.
yes
A square has diagonals that split the angles into two 45-degree parts, thus bisecting them.
* both pairs of opposite sides are parallel * both pairs of opposite sides are congruent * all angles are 90 degrees * both pairs of opposite angles are congruent * the diagonals 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