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
Answer: (D) any parallelogram
Solution.
Let ABCD is a rhombus and P, Q, R and S are its mid points.
In , R is the midpoint of AB and Q is the midpoint of BC.
and …..(1) {using mid-point theorem}
Similarly in
and …..(2)
From equation 1 and 2
and
Similarly when we take and then we get and .
Hence PQRS is a parallelogram
Therefore option (D) is correct.