Question

Two lines $AB$ and$CD$ intersect at $O$ such that $BC$ is equal and parallel to $AD$.
then $AB$ & $CD$ bisect at O.

• A. True
• B. False

Answer 1

The correct option is A True

Given:

$BC\parallel AD$.

Also in $\Delta AOD$ and $\Delta BOC$:

$AD=BC$......[given]

$\angle OAD=\angle OBC$......[alternate interior angles]

$\angle ODA=\angle OCB$......[alternate interior angles]

So, $\Delta AOD\cong \Delta BOC$....[by $ASA$ condition]

Hence $OA=OB$ and $OC=OD$....[By $CPCT$]

Hence $AB$ and $CD$ are bisected at $O$.