Points M and N are marked on the sides of the angle at an equal distance from its vertex O, and point P

Points M and N are marked on the sides of the angle at an equal distance from its vertex O, and point P is marked on the bisector of this angle. Prove the equality of triangles OMP and ONP.

Given:
angle MON,
OP is the bisector.
OM = ON.
Prove that triangle OMP is equal to triangle ONP.
Evidence:
Consider triangle OMP and triangle ONP. They have sides ОМ = ОN according to the condition of the problem, the angle MOP = PON because the ray OP is a bisector and splits the angle О into two equal angles. The OP side is common. Therefore, on two sides and the angle between them, the triangle OMP = the triangle ONP. Q.E.D.