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They are the same concept, one for the angle and 1 for triangle.Definition of a triangle angle bisector is a line segment that bisects one of the vertex angles of a triangle.Definition of an angle bisector is a ray or line segment that bisects the angle, creating two congruent angles.
The Angle Bisector Theorem states that given triangle and angle bisector AD, where D is on side BC, then . Likewise, the converse is also true. Not sure if this is what you want?
An angle bisector bisects an angle. A perpendicular bisector bisects a side.
Any shape which has an angle can have an angle bisector.
A segment need not be a bisector. No theorem can be used to prove something that may not be true!