Question

In the figure, E is the mid-point of side AD of a trapezium ABCD with AB || CD. A line through E parallel to AB meets
BC in F.

Then find which of the option is correct.

• A. $BF=\frac{1}{4}BC$
• B. $BF=\frac{1}{3}BC$
• C. $BF=\frac{1}{2}BC$
• D. $BF=\frac{1}{4}BA$

Answer 1

The correct option is C $BF=\frac{1}{2}BC$


Join AC to intersect EF at G.
EF || DC
$⟹$ EG ||DC

E is the mid point of AD and EG || DC.

$\therefore$G is the mid point of AC (By converse of mid point theorem)

In $△$ABC, FG || AB and G is the mid point of AC.

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

That is $BF=\frac{1}{2}BC$