In the below figure, 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 \(CD\).
Proof:
\(BC \parallel AD\) [Given]
\(\angle CBO\) \(=\) \(\angle\) [Alternative interior angle]
\(\angle BCO = \angle ADO\) []
\(BC = DA\) [Given]
\(\triangle BOC \cong \triangle AOD\) [By congruence rule]
Thus, \(OB = OA\) and \(OC = OD\).
Therefore, \(O\) is the mid-point of both the line-segments \(AB\) and \(CD\).