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  • The figure obtained by joining the mid-points of the sides of a rhombus, taken in order, is: (A) a rhombus (B) a rectangle (C) a square (D) any parallelogram

The figure obtained by joining the mid-points of the sides of a rhombus, taken in order, is:
(A) a rhombus            (B) a rectangle
(C) a square       (D) any parallelogram

Answers (1)

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Answer: (D) any parallelogram
Solution.
Let ABCD is a rhombus and P, Q, R and S are its mid points.

In \triangle ABC, R is the midpoint of AB and Q is the midpoint of BC.
AC\parallel RQ  and  RQ=\frac{1}{2}AC                …..(1) {using mid-point theorem}
Similarly in \triangle ADC
AC\parallel SP and  SP=\frac{1}{2}AC      …..(2)
From equation 1 and 2
SP\parallel RQ and SP=RQ
Similarly when we take \triangle ABDand \triangle BDC then we get  SR\parallel PQ and SR=PQ.
Hence PQRS is a parallelogram
Therefore option (D) is correct.

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