Question

answer attempt 1 out of 2

overline{fg} is a perpendicular bisector.
overline{fg} is an angle bisector.
f is the vertex of two angles that are congruent to one another.
f is the vertex of a right angle.
f is the midpoint of a segment in the diagram.
none of the above.

Explanation:

Step1: Analyze the definition of an angle bisector

An angle bisector is a ray that divides an angle into two congruent angles. In the diagram, since there are two congruent - marked angles at vertex \(F\) (the angle - marking indicates that \(\angle EFG\cong\angle DFG\)), and \(\overline{FG}\) is the ray that divides the angle at \(F\) into these two congruent parts.

Step2: Analyze other options

• For the perpendicular bisector: There is no indication (right - angle marks or equal - segment marks for a bisected segment) that \(\overline{FG}\) is a perpendicular bisector.
• For \(F\) being the vertex of a right - angle: There are no right - angle marks in the diagram.
• For \(F\) being the mid - point of a segment: There are no segment - length equal marks to suggest \(F\) is a mid - point of a segment.

Answer:

B. \(\overline{FG}\) is an angle bisector.
C. \(F\) is the vertex of two angles that are congruent to one another.