Question

Diagonals of a quadrilateral are perpendicular to each other.Is such a quadrilateral always a rhombus ? Give a figure to justify

Answer 1

If all sides of a quadrilateral are congruent, then it’s a rhombus (reverse of the definition). If the diagonals of a quadrilateral bisect all the angles, then it’s a rhombus (converse of a property). If the diagonals of a quadrilateral are perpendicular bisectors of each other, then it’s a rhombus (converse of a property).