1.

The quadrilateral formed by joining the mid-points of the sides of a quadrilateralPQRS, 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.

Answer»

(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.



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