The paper is focused on educational practices which may enable students to discover the property of interior angle bisector in a triangle with the help of exploration of dynamic constructions. Interactive geometry software is used for exploring relationships between geometrical objects, for transition from conjecture to verification of a statement, and for development of discovered relationships. Second part of the paper presents various methods to prove the formulated theorem based on the similarity of triangles, trigonometric law of sines, and analytic method.