Question

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

answer
$overline{eg}$ is a segment bisector.
$overline{eg}$ is a perpendicular bisector.
$overline{eg}$ is an angle bisector.
$e$ is the vertex of two angles that are congruent to one another.
$g$ is the vertex of two angles that are congruent to one another.
$e$ is the midpoint of a segment in the diagram.

Explanation:

1. An angle bisector divides an angle into two congruent angles. The diagram shows $\overline{EG}$ splits $\angle FED$ into two marked congruent angles, so $\overline{EG}$ is an angle bisector.
2. The two angles at vertex $E$ (split by $\overline{EG}$) are marked as congruent, so $E$ is the vertex of two congruent angles.
3. There is no indication $\overline{EG}$ bisects a segment, is perpendicular to a segment, that angles at $G$ are congruent, or that $E$ is a midpoint of any segment.

Answer:

$\overline{EG}$ is an angle bisector.
$E$ is the vertex of two angles that are congruent to one another.