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 2 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 the segment bisector

A segment bisector divides a segment into two equal parts. There is no indication that \(EF\) bisects any segment.

Step2: Analyze the congruent angles at \(E\)

There is no information given about angles at \(E\) being congruent.

Step3: Analyze the right - angle at \(E\)

There is no mark or indication that \(E\) is the vertex of a right - angle.

Step4: Analyze the mid - point of a segment

Since \(AE = EB\) (marked in the diagram), \(E\) is the mid - point of segment \(AB\).

Step5: Analyze the mid - point of a segment for \(F\)

There is no indication that \(F\) is the mid - point of any segment.

Answer:

\(E\) is the midpoint of a segment in the diagram.