Question

Which of the following statements must be true based on the diagram below? Select all that apply. (Diagram is not to scale.)

FG is a segment bisector.

FG is a perpendicular bisector.

F is the vertex of a pair of congruent angles in the diagram.

G is the vertex of a pair of congruent angles in the diagram.

G is the midpoint of a segment in the diagram.

None of the above.

Answer 1

The true statement that must be true based on the diagram is F-G is a segment bisector.

A segment bisector is a line, ray, or segment that divides another segment into two equal parts. Since it is mentioned as a segment bisector, it means that the line or segment "F-G" is dividing another segment into two equal parts. In other words, "F-G" is splitting a segment into two congruent (equal-length) segments.

For example, if there is a segment AB, and FG is a segment bisector of AB, it implies that A-F is equal in length to F-B. Mathematically, you can express this relationship as A-F = FB. The true statement that must be true based on the diagram is FG is a segment bisector.