Question

ABCD is a trapezium is which $AB\parallel DC$, BD is a diagonal and E is the midpoint of AD. A lie is drawn through E parallel. AB IN intersecting BC at F. show that F is the midpoint of BC

Answer 1

Given ABCD is a trapezium.

We have to prove, F is the mid point of BC, i.e., BF$=$CF

Let EF intersect DB at G.

In $\Delta$ABD E is the mid point of AD and EG$||$AB.

$\therefore$ G will be the mid-point of DB.

Now EF$||$AB and AB$||$CD

$\therefore$ EF$||$CD

$\therefore$ In $\Delta$BCD, GF$||$CD

$\Rightarrow$ F is the mid point of BC.