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Write the shape of the quadrilateral formed by joining the mid-points of the sides of a rhombus taken in order.

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Rectangle.

Square.

Rhombus.

Parallelogram.

answer is A.

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Detailed Solution

Given, a rhombus.
Question Image

Consider ABCD is a rhombus with points P, Q, R and S as mid-points of sides AB, BC, CD, AD respectively.
In

Δ A B C

, P is the mid-point of AB and Q is the mid-point of BC.
By mid-point theorem,

P Q ∥ A C, P Q = 12 A C

… (1)
Similarly,

S R ∥ A C, S R = 12 A C [By midpoint theorem]

… (2)
Thus,

P Q ∥ S R, P Q = S R

[From (1) and (2)]
Thus, PQRS is a parallelogram.
Also, ABQS is a parallelogram.

⇒ A B = S Q

[Opposite sides of parallelogram] … (3)
Similarly, PBCR is a parallelogram.

⇒ B C = P R [Opposite sides of parallelogram] ⇒ A B = P R [AB =BC, Sides of rhombus] ⇒ S Q = P R [From (3)]

So, the diagonals of a parallelogram are equal.
Hence, PQRS is a rectangle.
The quadrilateral is rectangle.
Hence, the correct option is 1.

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