In the adjoining figure, is a trapezium in which and is the midpoint of A line segment meets at Show that is the midpoint of

Question

Philoid · Accepted Answer

Here, ABCD is trapezium.

Join BD to cut EF at O.

It is given that, in ∆DAB, E is the mid point of AD and EO || AB.

∴ O is the midpoint of BD …By converse of mid point theorem

Now in ∆BDC, O is the mid point of BD and OF || DC.
∴ F is the midpoint of BC … By converse of mid point theorem