Question

In figure, two lines $AB$ and $CD$ intersect each other at the point $O$ such that $BC\parallel DA$. Show that $O$ is the mid-point of both the line-segments $AB$ and $CD$.

Answer 1

$\begin{array}{c}In\Delta COB\&\Delta AOD\left(verticallyoppositeange\right)\\ \angle COB=\angle AOD\left(alternateinteriorangle\right)\\ AB:BC\left(given\right)\\ \therefore \Delta COB\cong \Delta AOD\left(ASAcongurency\right)\\ \therefore OB:OA\left(CPCT\right)\\ andOC=OD\left(CPCT\right)\\ andhenceOisthemidpoint.\end{array}$