The figure formed by joining the midpoints of the sides of a quadrilateral ABCD, taken in order, is a square, only if

Question:

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

 

Solution:

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).

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