Answer :

The figure for the solution:

ABCD is a trapezium in which AB||DC.

Joining diagonal AC, which intersects EF at O.

In ΔADC, E is mid-point of AD and OE || CD.

By mid-point theorem, O is mid-point of AC.

Similarly,

In ΔCBA, O is mid-point of AC and OF||AB.

F is mid-point of BC by Mid-point Theorem.

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