ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Figure). AC is a diagonal. Show that :
(ii) PQ = SR
(iii) PQRS is a parallelogram.
In , S is the midpoint of DA and R is the midpoint of DC.
Therefore, by midpoint theorem, we have and
In , P is the midpoint of AB and Q is the midpoint of BC.
Therefore, by midpoint theorem, we have and (1)
We have already proved above in solution (i) that and . (2)
From (1) and (2), we can say that
From (1) and (2) above, we can say that and
is a parallelogram.
(A quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel.)