Question

which of the following statements must be true based on the diagram below? select all that apply.
answer attempt 1 out of 2
\\(\overline{fg}\\) is a segment bisector.
\\(\overline{fg}\\) is a perpendicular bisector.
\\(\overline{fg}\\) is an angle bisector.
\\(f\\) is the vertex of a right angle.
\\(g\\) is the vertex of a right angle.
\\(g\\) is the midpoint of a segment in the diagram.

Explanation:

Step1: Analyze segment - bisector definition

A segment - bisector divides a segment into two equal parts. There is no indication in the diagram that $\overline{FG}$ divides any segment into two equal parts. So, $\overline{FG}$ is not a segment bisector.

Step2: Analyze perpendicular - bisector definition

A perpendicular bisector is a line or segment that is perpendicular to another segment and also bisects it. There is no indication of perpendicularity or bisection of a segment by $\overline{FG}$ in the diagram. So, $\overline{FG}$ is not a perpendicular bisector.

Step3: Analyze angle - bisector definition

An angle bisector divides an angle into two equal angles. There is no indication in the diagram that $\overline{FG}$ divides any angle into two equal angles. So, $\overline{FG}$ is not an angle bisector.

Step4: Analyze right - angle vertex

There is no right - angle symbol at either $F$ or $G$ in the diagram, so $F$ is not the vertex of a right - angle and $G$ is not the vertex of a right - angle.

Step5: Analyze mid - point

There is no indication in the diagram that $G$ is the mid - point of any segment.

Answer:

None of the statements are true.