Given
P, Q, R and S are the mid points of quadrilateral ABCD
Solution
Theorem :The line segment joining the mid-points of two sides of a triangle is parallel to the third side.
(i) SR || AC and SR = 1/2 AC
Considering ∆ACD
we observe that S and R are the mid points of side AD and DC respectively. [Given]
Hence,SR || AC and SR = ½ AC (As per the above theorem)……………………….(1)
(ii) PQ = SR
Considering ∆ACB
We observe that P and Q are the mid points of side AB and BC respectively. [Given]
Hence, PQ || AC and PQ = ½ AC (As per above theorem)…………………………(2)
From (1) and (2) we can say,
PQ = SR
(iii) PQRS is a parallelogram
rom (i) and (ii) we can say that
PQ || AC and SR || AC
so, PQ || SR and PQ = SR
If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.
Hence, PQRS is a parallelogram.