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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
(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
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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).
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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