Question

The figure formed by joining the midpoints of the adjacent sides of a parallelogram is a

(a) rhombus

(b) square

(c) rectangle

(d) parallelogram

Answer 1

Consider a parallelogram ABCD as follows:

As we know that the opposite sides of a parallelogram is parallel.
So $AB\parallel DC$ and $AD\parallel BC$
Consider a triangle $\Delta DBC$, from mid point theorem, we have
$DB\parallel RQ$ ......(i)
From triangle $\Delta DBA$, we $DB\parallel SP$....(ii)
Thus, $RQ\parallel SP$
Similar way we can prove $PQ\parallel SR$
Thus, PQRS is a quadrilateral whose opposite sides are parallel.
Therefore, PQRS is parallelogram.
Hence, the correct option is (d) (Parallelogram)