**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.