In the figure, The bisector \(PY\) cuts \(\angle RPQ\) in half, and \(PR = PQ\). Prove that \(\triangle PRY \cong \triangle PQY\).
Proof:
Consider the triangles \(PRY\) and \(PQY\).
\(PR =\) ()
\(\angle RPY = \angle \) ()
\(PY = \) ()
Thus, \(\triangle PRY \cong \triangle PQY\) (by congruence rule).