Question -
Answer -
ABCD is a parallelogram, AD produced to E such that .
Also , AB produced to F.
We need to prove that
In
, D and O are the mid-points of AE and AC respectively.By using Mid-point Theorem, we get:
Since, BD is a straight line and O lies on AC.
And, C lies on EF
Therefore,
…… (i)
Also,
is a parallelogram with 
.Thus,
In
and 
,we have:So, by ASA Congruence criterion, we have:
By corresponding parts of congruence triangles property, we get:
From (i) equation, we get:
Hence proved.