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 { l n } $ is a segment bisector.
$ \overline { l n } $ is a perpendicular bisector.
$ \overline { l n } $ is an angle bisector.
$ n $ is the vertex of two angles that are congruent to one another.
$ n $ is the vertex of a right angle.
$ n $ is the midpoint of a segment in the diagram.

Question

Accepted Answer

# Explanation:
## Step1: Recall the definition of a mid - point
A mid - point of a line segment divides the line segment into two equal parts. In the diagram, since $N$ is the mid - point of a segment (implied by the markings on the segment $KJ$ where $KN = NJ$), the statement “$N$ is the mid - point of a segment in the diagram” is True.
## Step2: Analyze the other statements
- For a perpendicular bisector: There is no indication (such as a right - angle symbol) that $\overline{LN}$ is perpendicular to $KJ$, so “$\overline{LN}$ is a perpendicular bisector” is False.
- For an angle bisector: There is no indication (such as congruent angle markings) that $\overline{LN}$ bisects an angle at $N$, so “$\overline{LN}$ is an angle bisector” is False.
- For $N$ being the vertex of a right - angle: There is no right - angle symbol at $N$, so “$N$ is the vertex of a right - angle” is False.
- For $N$ being the vertex of two congruent angles: There is no angle - marking information to support this, so “$N$ is the vertex of two angles that are congruent to one another” is False.

# Answer:
$N$ is the mid - point of a segment in the diagram.

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the definition of a mid - point

Step2: Analyze the other statements

Answer: