Question

Line segment $AB$ is parallel to another line-segment $CD$,$O$ is the midpoint of $AD$.Show that $△AOB\cong △DOC$

Answer 1

In $△AOB$ and $△DOC$

$\angle BAO=\angle CDO$ (alternate angles as $AB\parallel CD$ and $BC$ is the transversal)

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

$OA=OD$(given)

$\therefore △AOB\cong △DOC$ by ASA rule.