Definitions:
Perpendicular bisector: A line that bisects (split into two equal parts) a line segment at a right angle (90°)
Angle bisector: A line that bisects a angle.
Median of a triangle: Line segment drawn from a vertex to the middpoint of the opposite side to the vertex.
Altitude of a triangle: Perpendicular segment form a vertex of a triangle to the opposite side.
a) With the given information you can describe FI as:
Median of triangle FGH:
Line segment drawn from a vertex (F) to the middpoint of the opposite side to the vertex (GH). The two marks in red indicates that the segments have the same measure (then the point I is the middpoint of the side GH.
Theres is not indication of a perpendicular angle, or a bisection of the angle. Then you can not describe FI as any of the other options.