Question

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

$overline{ef}$ is a segment bisector.
$e$ is the vertex of two angles that are congruent to one another.
$e$ is the vertex of a right - angle.
$e$ is the midpoint of a segment in the diagram.
$f$ is the midpoint of a segment in the diagram.
none of the above.

Explanation:

Step1: Analyze segment - bisector claim

There is no indication in the diagram that $\overline{EF}$ divides any segment into two equal - length parts, so $\overline{EF}$ is not necessarily a segment bisector.

Step2: Analyze angle - congruence claim

There is no information in the diagram to suggest that the angles with vertex $E$ are congruent.

Step3: Analyze right - angle claim

There are no right - angle markings at vertex $E$, so we cannot say $E$ is the vertex of a right angle.

Step4: Analyze mid - point claims

The tick marks on $\overline{AB}$ show that $E$ is the mid - point of $\overline{AB}$ since the two sub - segments $\overline{AE}$ and $\overline{EB}$ are congruent. There is no indication that $F$ is the mid - point of any segment in the diagram.

Answer:

$E$ is the midpoint of a segment in the diagram.