P, Q, R, S are respectively the midpoints of the sides AB, BC, CD and DA of ||gm ABCD. Show that PQRS is a parallelogram and also show that ar(||gm PQRS)=12ar(||gm ABCD).

P, Q, R, S are respectively the midpoints of the sides AB, BC, CD and

1.	P, Q, R, S are respectively the midpoints of the sides AB, BC, CD and DA of \|\|gm ABCD. Show that PQRS is a parallelogram and also show that ar(\|\|gm PQRS)=12ar(\|\|gm ABCD).
Answer» P, Q, R, S are respectively the midpoints of the sides AB, BC, CD and DA of \|\|gm ABCD. Show that PQRS is a parallelogram and also show that $a r (\| \| g m P Q R S) = \frac{1}{2} a r (\| \| g m A B C D)$ .