Answer :

__Given :-__ ABCD is a parallelogram

And CE=EB

__Formula used:-__ ASA congruency property

If 2 angles and one side between them in two

triangles are equal then both triangle are congruent

__Solutions :-__

In Δ DCE and Δ FBE

∠ DEC=∠ BEF [Vertically opposite angles]

As DC || BF

∠ ECD=∠ EBF [Alternate angles]

And;

CE=EB [Given]

∴ Δ DCE ≅ Δ FBE

As Δ DCE ≅ Δ FBE

Then

DC=BF

And DC=AB [opposite sides of parallelogram are equal]

Hence ;

AB=BF

AF=AB+BF

AF=2AB.

Hence Proved;

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