Question

Line-segment $AB$ is parallel to another line-segment $CD.O$ is the mid-point of $AD$.
Show that $O$ is also the midpoint of $BC$.

Answer 1

Given: AB is parallel to another line segment CD.

O is the midpoint OF AD

In $\Delta AOB$ and $\Delta DOC$

$\angle AOB=\angle COD$ ...(Vertically opposite angle )

$\angle BAO=\angle CDO$ ...(Given AB parallel to DC and AD meet both lines so alternate angles are equal)

$AO=OD$ ....(O is the midpoint of AD )

$\Delta AOB\cong \Delta DOC$ ...ASA test

So, $BO=CO$

Then, O is the midpoint of BC.