Question

which of the following statements must be true based on the diagram below? select all that apply. (diagram is not to scale.) answer attempt 1 out of 2
$overline{fh}$ is a segment bisector.
$overline{fh}$ is an angle bisector.
$h$ is the vertex of two angles that are congruent to one another.
$f$ is the midpoint of a segment in the diagram.
$h$ is the midpoint of a segment in the diagram.
none of the above.

Explanation:

Step1: Analyze segment - bisector

Since $DH = HE$, $\overline{FH}$ divides segment $\overline{DE}$ into two equal - length parts. So, $\overline{FH}$ is a segment bisector.

Step2: Analyze angle - bisector

There is no information indicating that $\overline{FH}$ divides an angle into two equal parts. So, we cannot say $\overline{FH}$ is an angle bisector.

Step3: Analyze congruent angles at $H$

There is no information suggesting that the angles with vertex $H$ are congruent.

Step4: Analyze mid - point at $F$

There is no information showing that $F$ is the mid - point of a segment.

Step5: Analyze mid - point at $H$

Since $DH = HE$, $H$ is the mid - point of $\overline{DE}$.

Answer:

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