4. ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F (see Fig. 8.30). Show that F is the mid-point of BC.
Solution: Given that, ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD. To prove, F is the mid-point of BC. Proof, BD intersected EF at G. In ΔBAD, E is the mid point of AD and also EG || AB. Thus, G is the mid point of BD (Converse of mid point theorem) Now, In ΔBDC, G is the mid point of BD and also GF || AB || DC. Thus, F is the mid point of BC (Converse of mid point theorem)
