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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
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
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Solution
ANSWER:
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).
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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