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 { e f } \\) 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 information in the diagram to suggest that \( \overline{EF} \) bisects any segment.

Step2: Analyze angles at vertex \( E \)

There is no indication in the diagram that \( E \) is the vertex of two congruent angles.

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

There is no right - angle symbol at \( E \), so we cannot assume \( E \) is the vertex of a right - angle.

Step4: Analyze mid - point at \( E \)

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

Step5: Analyze mid - point at \( F \)

There is no information in the diagram to suggest that \( F \) is the midpoint of any segment.

Answer:

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