Question

23)
In the given figure ABCD is a trapesium
in which AB || DC and E is the mid point of AD. A line segment EF which is parallel AB intersects BC at F . Show
that F is the mid point of BC​

Answer 1

$\Large\underline{\underline{\sf \blue{Given:}}}$

We have AB, EF and CD parallel lines.

$\Large\underline{\underline{\sf \blue{To\: Prove:}}}$

We have to prove that F is the mid point of the side BC.

$\Large\underline{\underline{\sf \blue{Solution :}}}$

Construction : - Join the points A and C to form diagonal AC.

In triangle ADC, according to the mid point theorem,

$\implies$EG parallel to DC

$\implies$ E is the midpoint AD

$\implies$ G is the mid point of AC

$\implies$ Now, in triangle ABC, according to the mid point theorem,

$\implies$ GF parallel to AB

$\implies$ G is the midpoint AC

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