Question -
Answer -
Figure is given as follows:
It is given that ABCD is a parallelogram.
DE and AB when produced meet at F.
We need to prove that
It is given that
Thus, the alternate interior opposite angles must be equal.
In
and 
, we have 
(Proved above) 
(Given) 
(Vertically opposite angles) Therefore,
(By ASA Congruency ) By corresponding parts of congruent triangles property, we get
DC = BF …… (i)
It is given that ABCD is a parallelogram. Thus, the opposite sides should be equal. Therefore,
…… (ii) But,
From (i), we get:
From (ii), we get:
Hence proved.