if P,Q,R,S be respectively the midpoints of the sides AB,BC,CD and DA of a quadrilateral ABCD. Show that PQRS is a parallelogram such that ar(PQRS)=1/2 ar(ABCD)
R and S are mid-points of the sides CD and DA of triangle ACD
=> RS is parallel to side AC of triangle ACD and of length = (1/2)AC
=> PQ and RS which are the opposite sides of the quadrilateral PQRS are of equal length and both being parallel to AC are parallel to each other.
=> quadrilateral PQRS is a parallelogram.
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