In the figure given above, \(PO\) is the angle bisector of \(\angle RPQ\), and \(PR = PQ\). Prove that \(\triangle PRO \cong \triangle PQO\).
Proof :
let us consider the triangles \(RPO\) and \(OPQ\)
\(PR=\)
\(\angle RPO = \angle\)
\(PO=\)
Thus by congruence criterion, the triangles \(RPO\) and \(OPQ\) are congruent to each other.
That is, \(\triangle RPO \cong \triangle OPQ\).