Question

AB and CD intersect each other at O and O is the midpoint of both AB and CD. Prove that AD=BC.

Answer 1

Given $O$ is the mid point of $AB$ and $CD$

$⟹OA=OB,OC=OD$

In $△AOD,△BOC$

$AO=BO,CO=DO,\angle AOD=\angle BOC\left(verticallyoppositeangles\right)$

By $S.A.S$ congruency

$△AOD\cong △BOC$

$⟹AD=BC$