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
$overline{ef}$ 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 property

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

Step2: Analyze angle - congruence at point E

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

Step3: Analyze right - angle at point E

There is no right - angle symbol or any information to imply that $E$ is the vertex of a right - angle.

Step4: Analyze mid - point property of E

Since there are tick marks indicating that $AE = EB$, $E$ is the mid - point of segment $\overline{AB}$.

Step5: Analyze mid - point property of F

There is no information to suggest that $F$ is the mid - point of any segment in the diagram.

Answer:

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