Two lines \(l\) and \(m\) intersect at the point \(O\) and \(P\) is a point on a line \(n\) passing through the point \(O\) such that \(P\) is equidistant from \(l\) and \(m\). Prove that \(n\) is the bisector of the angle formed by \(l\) and \(m\).
Proof :
\(\triangle OQP \cong \triangle ORP\) [By Congruence rule]
\(\angle POQ = \angle POR\) [By ]
Therefore, \(n\) is the bisector of the angle formed by \(l\) and \(m\).
Hence, we proved.