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.
no
A parallelogram.
True
Yes. Because the diagonals are perpendicular to each other and intersect at their midpoints, they bisect each other.
may or may not be
square
False
no
false
A parallelogram.
A rectangle or a parallelogram
No. It is false. If both of those conditions are met, then the quadrilateral is a square.
True
True
False. Bisecting diagonals is sufficient to guarantee a parallelogram, but the diagonals will only be perpendicular if the sides of the parallelogram are equal.
True
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