Question

In fig 7.1, two lines AB and CD intersect each other at the point O such that $BC\parallel DA$ and $BC=DA$.
Show that O is the mid point of both the line-segments AB and CD.

Answer 1

In $△OBC$ and $△OAD$

$BC=DA$ ....... (Given)

$\angle OCB=\angle ODA$ ....... $(\because CB\parallel DA$, so alternate opposite angles are equal)

$\angle OBC=\angle OAD$ ...... $(\because CB\parallel DA$, so alternate opposite angles are equal)

$\therefore △OBC\cong △OAD$ (By ASA criterion)

Thus, $CO=DO$ and $BO=AO$ (By C.P.C.T.C.)

$\Rightarrow$ So, $O$ is the midpoint of $AB$ and $CD$.