Final Answer:
The segment that is a perpendicular bisector of triangle ABC is Segment SB (Option b).
Step-by-step explanation:
A perpendicular bisector of a triangle is a line segment that both bisects one of the triangle's sides and is perpendicular to it. In this case, Segment SB is identified as the perpendicular bisector because it bisects side AC (the side opposite angle B) and is perpendicular to it. This is a key property of perpendicular bisectors in triangles (Option b).
To confirm this, one can examine the angles formed between Segment SB and sides AB and BC. If Segment SB is a perpendicular bisector, the angles formed with these sides will be right angles. The perpendicularity ensures that the triangle is divided into two congruent right-angled triangles.
This property is essential in geometry, particularly in the context of triangles, as perpendicular bisectors play a crucial role in defining the circumcenter of a triangle. The circumcenter is the point where the perpendicular bisectors of a triangle intersect, and it has equidistant relationships to the triangle's vertices. Understanding these geometric relationships aids in solving various problems and proofs involving triangles and their associated line segments.