Question

answer attempt 2 out of 2
(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:

Step1: Identify angle - marking

The two equal - angle markings at vertex $E$ indicate that $\overline{EG}$ divides an angle at $E$ into two equal angles.

Step2: Recall definitions

An angle bisector is a ray or line segment that divides an angle into two congruent angles. Since $\overline{EG}$ divides an angle at $E$ into two congruent angles, $\overline{EG}$ is an angle bisector. Also, $E$ is the vertex of two angles that are congruent to one another.

Answer:

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