It has been proven below that BF ║ CD.
From the given diagram, we are told that;
ΔABF ≅ ΔBCD
This means both triangles are congruent.
Now, in the two triangles, we can see that;
∠BAF ≅ ∠CBD
Because they are corresponding angles
We also see that;
∠ABF ≅ ∠BCD
Because they are corresponding angles
Since point B is the midpoint of AC, then it means that;
AB = BC
Thus, we can see that 2 corresponding angles are equal and the included corresponding side is also equal and as a result this fulfils the ASA Congruency Postulate.
Thus, for the fact that ∠ABF ≅ ∠BCD, it means that BF must be parallel to CD.
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