Given : A trapezium ABCD with AB || DC, E is the mid-point of AD and EF || AB.
To Prove : F is the mid-point of BC.
Proof : AB || DC and EF || AB
⇒ AB, EF and DC are parallel.
Intercepts made by parallel lines AB, EF and DC on transversal AD are equal.
∴ Intercepts made by those parallel lines on transversal BC are also equal.
i.e., BF = FC
⇒ F is the mid-point of BC.