Question

In Fig. 8, 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. Show that F is the mid-point of BC.

Answer 1

Given: In trapezium ABCD, AB || DC, EF || AB and E is the mid-point of AD.

To prove: F is the mid-point of BC.

Proof:

In ΔABD,

As, EP || AB and E is the mid-point of AD (Given: EF || AB)

Therefore, by converse of mid-point theorem − The line drawn through the mid-point of one side of a triangle and parallel to another side bisects the third side, we get

P is the mid-point of BD

Now, similarly in ΔBCD,

As, PF || DC and P is the mid-point of BD (Since, EF || AB || CD)

Therefore, F is the mid-point of BC.