Question

The figure formed by joining the mid-points of the adjacent sides of a parallelogram is a

(a) rectangle

(b) parallelogram

(c) rhombus

(d) square

Answer 1

It is given a parallelogram ABCD in which P,Q,R and S are the mid-points AB, BC, CD and DA respectively.

PQ, QR, RS and SP are joined.

In , P and Q are the mid-points AB and BC respectively.

Therefore,

and ……(i)

Similarly, In , R and S are the mid-points CD and AD respectively.

Therefore,

and ……(ii)

From (i) and (ii), we get

and

Therefore, is a parallelogram.

Hence the correct choice is (b).