The segments AB and AD are equal, AO is the bisector of the angle BAD, C is an arbitrary point

The segments AB and AD are equal, AO is the bisector of the angle BAD, C is an arbitrary point of the ray AO. Prove the equality of triangles ABC and ADC.

Given:
angle BAD,
AO – bisector of the angle BAD,
point C belongs to the bisector AO,
AB = AD.
Prove the equality of triangles ABC and ADC.
Evidence:
Consider triangle ABC and triangle ADC. They have a common side of AO. Angle BAD = angle OAD, since AO is the bisector of BAD and bisects this angle. Sides AB = AD according to the problem statement. Therefore, on two sides and the angle between them, the triangle ABC = triangle ADC. Q.E.D.