YA is not an angle bisector because it is not contained in the same plane . If <XYZ is less than 180 and you place A in the exterior of <XYZ so that <AYX and <AYZ are congruent obtuse angles you MIGHT be able to argue that SEGMENT (or ray) YA does not bisect the original <XYZ.
* There really isn’t a good answer to this question . I talked to two different math teachers and they said the same .