Given: ABCD is a trapezium in which AB || DC and EF||AB|| CD.
Construction: Join, the diagonal AC which intersects EF at O.
To show: F is the mid-point of BC.
Proof: Now, in ΔADC, E is the mid-point of AD and OE || CD. Thus, by mid-point theorem, O is mid-point of AC.
Now, in ΔCBA, 0 is the mid-point of AC and OF || AB.
So, by mid-point theorem, F is the mid-point of BC.