Q6 of 109 Page 314

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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