Question

Line-segment $AB$ is parallel to another line-segment $CD.O$ is the mid-point of $AD$.
Show that:
(a) $△AOB\cong △DOC$
(b) $O$ is also the mid-point of $BC$.

Answer 1

Consider $△AOB$ and $△DOC$.

$\angle ABO=\angle DCO$ (Alternate angles as $AB\parallel CD$ and

$BC$ is the transversal)

$\angle AOB=\angle DOC$ (Vertically opposite angles)

$OA=OD$ (Given)

Therefore, $△AOB\cong △DOC$ (AAS rule)

By $CPCTO$ is midpoint of $BC$