In fig $A B = C F, E F = B D$ and $A F E = ∠ C B D$ prove that
$△ A F E = △ C B D$

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Solution

In $Δ A F E$
$A F = A C - C F = A C - A B - - (1)$ [ $A B = C F$ is given]
In $Δ C B D$
$C B = C A - B A - - - (2)$
From $(1)$ and $(2)$
$A F = C B - - I$
Now in $Δ A F E$ and $Δ C B D$
$, E F = D B$ [Given} $A F E = ∠ C B D$ [Given]
$A F = C B$ [From $I$ ]
Hence $△ A F E = △ C B D$

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A B = C F, E F = B D

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