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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