(r. Consider triangle ACD,
121
S and R are mid-points of sides AD and DC respectively.
•••(i) [Line segment joining mid-points of two sides of a triangle is parallel to the third and half of it.]
(ii) Consider triangle ABC, P and Q are mid-points of
sides AB and BC respectively.
1
:. PQ II AC and PQ = -AC
2
•••(ii)
[Reason same as above]
From (i) and (ii),
SR 11 AC and PQ II AC SR 11 PQ ...(iii)
and• . SR = iAc and PQ = iAc SR = PQ. ...(iv)
(iii) • SR 11 PQ and SR = PQ. [From (iii) and (iv>1
PQRS is a parallelogram.
We know that diagonals of a parallelogram bisect each other, i.e.,
OP = OR and OQ = OS.
Hence, line segments joining mid points of opposite sides of a quadrilat.eral bisect each other.
