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
$overline{mn}$ is a segment bisector.
$overline{mn}$ is a perpendicular bisector.
$m$ is the vertex of a right angle.
$n$ is the vertex of a right angle.
$m$ is the midpoint of a segment in the diagram.
$n$ is the midpoint of a segment in the diagram.

Explanation:

Step1: Identify midpoints

From the diagram, $N$ splits $\overline{KL}$ into two congruent segments, so $N$ is the midpoint of $\overline{KL}$. $M$ splits $\overline{JL}$ into two congruent segments, so $M$ is the midpoint of $\overline{JL}$.

Step2: Analyze segment bisector

A segment bisector divides a segment into two congruent parts. $\overline{MN}$ does not bisect any shown segment, so it is not a segment bisector.

Step3: Analyze perpendicular bisector

There is no indication $\overline{MN}$ is perpendicular to any segment, so it is not a perpendicular bisector.

Step4: Analyze right angles

No right angle symbols are present at $M$ or $N$, so they are not right angle vertices.

Answer:

M is the midpoint of a segment in the diagram.
N is the midpoint of a segment in the diagram.