Question

In the given figure ABCD is a parallelogram and E is the mid point of the side BC. If DE and AB are produced to meet at F, show that AF = 2AB.

Answer 1

Given that □ABCD is a parallelogram. 

E is the midpoint of BC. 

Let G be the midpoint of AD.

Join G, E.

Now in ΔAFD, GE is the line joining the midpoints G, E of two sides AD and FD.

∴GE // AF and GE = 1/2 AF

But GE = AB [ ∵ ABEG is a parallelogram and AB, GE forms a pair of opp. sides]

1/2 = AB ⇒ AF = 2AB

Hence Proved.