In the adjoining figure, 
is a parallelogram. 
is the midpoint of 
and through 
a line segment is drawn parallel to 
to meet 
produced at 
and it cuts 
at 
Prove that
(i) 
(ii) 
ABCD is parallelogram.
(i) In ∆ DCG, we have:
DG || EB
DE = EC … E is the midpoint of DC)
Also, GB = BC … by midpoint theorem
∴ B is the midpoint of GC.
Also, GC = GB + BC
GC = 2BC
GC = 2 AD …as AD = BC
∴ AD = 
GC
(ii) Now, in ∆ DCG, DG || EB and E is the midpoint of DC and B is the midpoint of GC.
∴ EB = 
DG … by midpoint theorem
∴ DG = 2 EB
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