'Right parallelogram', also called 'rectangle'.
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Not necessarily - the diagonals of a rhombus bisect each other (they are perpendicular bisectors of each other), but are not equal.
An isosceles trapezoid, or any trapezoid, does not have diagonals that bisect each other.
No.
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
Quadrilaterals do not bisect each other. They could in special cases. In parallelograms (types of quadrilaterals), the diagonals bisect each other.