What is the distinction between a bisector of an angle and an angle bisector of a triangle?

please help me finding the distinction?im little bit confused...

thank you so much

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- Jan 17th 2011, 05:21 AMjam2011Angle bisector
What is the distinction between a bisector of an angle and an angle bisector of a triangle?

please help me finding the distinction?im little bit confused...

thank you so much - Jan 17th 2011, 05:37 AMPlato
- Jan 17th 2011, 06:07 AMHallsofIvy
There is, of course, no distinction between the words "bisector of an angle" and "angle bisector". The only difference between the two phrases you give are the words "of a triangle". To have a "bisector of an angle" (or "angle bisector") you only have to have an angle- there may be no "triangle" involved. To have an "angle bisector of a triangle" (or "bisector of an angle of a triangle") you have to have a

**triangle**and, since a triangle has three angles, either specify which angle or make it clear that it could be any one of the angles. At that point you are talking about the bisector of that specific angle. - Jan 17th 2011, 07:26 AMjam2011
ACCording to the definition of the book: a segment is an angle bisector of a triangle if (1) it lies in the ray which bisect an angle of the triangle, and (2) its end points are the vertex of this angle and a point of the opposite side.

- Jan 17th 2011, 07:48 AMPlato
Well there you have it. For that particular author the phrase

*angle bisector of a triangle*mean a certain**line segment**which is a subset if the general angular bisector, the coplanar ray which makes angles of equal measure with the sides of an angle.

As a*line segment*the*angle bisector of a triangle*has a finite length unlike a*ray*. For some authors that is an important distinction.