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Question

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

(a) ABCD is a parallelogram

(b) ABCD is a rectangle

(c) diagonals of ABCD are equal

(d) diagonals of ABCD are perpendicular to each other

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Solution

ANSWER:
Since,
The quadrilateral formed by joining the mid-points of the sides of a parallelogram is parallelogram.
The quadrilateral formed by joining the mid-points of the sides of a rectangle is rhombus.
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 to each other is rectangle.
Hence, the correct option is (d).


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