In the figure, ABCD is a trapezium in which AB∥DC. E is the midpoint of AD and F is a point on BC such that EF ∥ DC. Show that F bisects BC.
join a diagonal, say AC to intersect AC at M. In triangle ADC, E is the mid point of AD and EM is parallel to DC. By mid-point theorem we know that M is the mid-point of AC. Now in triangle ABC, M is the mid-point of AC and MF is parallel to DC. By applying mid-point theorem, we can say that F is the mid-point of BC.