The figure formed by joining the midpoints of the sides of a quadrilateral ABCD, taken in order, is a square, only if
The figure formed by joining the midpoints of the sides of a quadrilateral ABCD, taken in order, is a square, only if
(a) ABCD is a rhombus
(b) diagonals of ABCD are equal
(c) diagonals of ABCD are perpendicular
(d) diagonals of ABCD are equal and perpendicular
Since,
The quadrilateral formed by joining the mid-points of the sides of a rhombus is rectangle,
The quadrilateral formed by joining the mid-points of the sides of a quadrilateral with diagonals equal is rhombus,
The quadrilateral formed by joining the mid-points of the sides of a quadrilateral with diagonals perpendicular is rectangle, and
The quadrilateral formed by joining the mid-points of the sides of a quadrilateral with diagonals equal and perpendicular is square.
Hence, the correct option is (d).