Question

answer attempt 2 out of 2
$overline{hi}$ is a segment bisector.
$overline{hi}$ is a perpendicular bisector.
$i$ is the vertex of two angles that are congruent to one another.
$i$ is the vertex of a right angle.
$h$ is the midpoint of a segment in the diagram.
$i$ is the midpoint of a segment in the diagram.

Explanation:

1. $\overline{HI}$ is a segment bisector: A segment bisector divides a segment into two equal parts. $\overline{HI}$ meets $\overline{DE}$ at $H$, which marks $\overline{DE}$ into two equal segments, so this is true.
2. $\overline{HI}$ is a perpendicular bisector: A perpendicular bisector must be perpendicular to the segment and bisect it. $\overline{HI}$ is perpendicular to $\overline{DE}$ (marked by the right angle symbol) and bisects it, so this is true.
3. $I$ is the vertex of two congruent angles: There is no marking or evidence in the diagram that $I$ forms two congruent angles, so this is false.
4. $I$ is the vertex of a right angle: The right angle symbol is at $H$, not $I$, so this is false.
5. $H$ is the midpoint of a segment in the diagram: $H$ divides $\overline{DE}$ into two equal segments, so $H$ is the midpoint of $\overline{DE}$, this is true.
6. $I$ is the midpoint of a segment in the diagram: $I$ divides $\overline{GF}$ into two equal segments, so $I$ is the midpoint of $\overline{GF}$, this is true.

Answer:

$\overline{HI}$ is a segment bisector.
$\overline{HI}$ is a perpendicular bisector.
$H$ is the midpoint of a segment in the diagram.
$I$ is the midpoint of a segment in the diagram.