Not a quadrilateral. But "Yes" to a rhombus and a rectangle. And, since a square is a rectangle as well as a rhombus, a square as well.
The diagonals of any parallelogram (square, rhombus, rectangle, rhomboid) bisect each other. The difference is the the diagonals are equal in length for a square and rectangle, and not equal for a rhombus or rhomboid (oblique diamond).
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
If you are talking about the diagonals of a quadrilateral, the only quadrilateral that have diagonals that are perpendicular and bisect each other is a square, because a rectangle has bisecting diagonals, while a rhombus has perpendicular diagonals. And a square fits in both of these categories.
A quadrilateral is a type of polygon that has four corners and sides. It is called a parallelogram (rectangle, square, or rhombus) when its diagonals bisect to each other.
The diagonals will not always bisect opposite angles in a rectangle.
Parallelogram and rhombus.
This occurs in a rhombus, rectangle, parallelogram, and a square (which is a type of rhombus).
The statement cannot be proved because it is not true.As a counter example, consider a parallelogram which is not a rhombus. Its diagonals do bisect each other but, by definition, it is not a rhombus.
Rectangle Parallelogram Square Rhombus
It is a rhombus or a kite
The diagonals of a rectangle bisect the angles only if the rectangle is a square.