Question

In the adjoining figure, ABCD is a trapezium in which AB || DC and E is the midpoint of AD. A line segment EF || AB meets BC at F. Show that F is the midpoint of BC.

Answer 1

Join BD to cut EF at M.
Now, in ∆DAB, E is the mid point of AD and EM || AB.
∴ M is the midpoint of BD. (By converse of mid point theorem)

Again, in ∆BDC, M is the mid point of BD and MF || DC.
∴ F is the midpoint of BC. (By converse of mid point theorem)