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The quadrilateral formed by joining the mid-points of the sides of a quadrilateral
PQRS, taken in order, is a rhombus, if
(A) PQRS is a rhombus
(B) PQRS is a parallelogram
(C) diagonals of PQRS are perpendicular
(D) diagonals of PQRS are equal.
The quadrilateral formed by joining the mid-points of the sides of a quadrilateral
PQRS, taken in order, is a rhombus, if
(A) PQRS is a rhombus
(B) PQRS is a parallelogram
(C) diagonals of PQRS are perpendicular
(D) diagonals of PQRS are equal.
The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if:
(A) PQRS is a rectangle
(B) PQRS is a parallelogram
(C) diagonals of PQRS are perpendicular
(D) diagonals of PQRS are equal
The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if:
(A) PQRS is a rectangle
(B) PQRS is a parallelogram
(C) diagonals of PQRS are perpendicular
(D) diagonals of PQRS are equal
(D) diagonals of PQRS are equal.
Explanation:
Since, ABCD is a rhombus
We have,
AB = BC = CD = DA
Now,
Since, D and C are midpoints of PQ and PS
By midpoint theorem,
We have,
DC = ½ QS
Also,
Since, B and C are midpoints of SR and PS
By midpoint theorem
We have,
BC = ½ PR
Now, again, ABCD is a rhombus
∴ BC = CD
⇒ ½ QS = ½ PR
⇒ QS = PR
Hence, diagonals of PQRS are equal
Therefore, option (D) is the correct answer.