Question

Line-segment AB is parallel to another line-segment CD. O is the midpoint of AD.
Show that
$\text{(i)}△AOB\cong △DOC$
(ii) O is also the midpoint of BC.

Answer 1

$\text{(i) Consider}△AOB\text{and}△DOC.$
$\angle ABO=\angle DCO\text{( Alternate angles as}AB||CD\text{and}$BC is the transversal)
$\angle AOB=\angle DOC\text{(Vertically opposite angles)}$
OA = OD (Given)
$\text{Therefore,}△AOB\cong △DOC\text{(AAS rule)}$
$\text{(ii)}OB=OC\left(CPCT\right)$
So, O is the midpoint of BC.