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
$overline{op}$ is a segment bisector. $overline{op}$ is an angle bisector. $o$ is the vertex of two angles that are congruent to one another. $o$ is the mid - point of a segment in the diagram. $p$ is the mid - point of a segment in the diagram. none of the above.

Explanation:

Step1: Define segment bisector

A segment bisector divides a segment into two equal - length segments. Since we have no information about lengths of segments divided by $\overline{OP}$, we can't say $\overline{OP}$ is a segment bisector.

Step2: Define angle bisector

An angle bisector divides an angle into two equal - measure angles. There is no indication that $\overline{OP}$ divides any angle into two equal parts, so we can't say $\overline{OP}$ is an angle bisector.

Step3: Analyze point O

There is no information suggesting that point O is the vertex of two congruent angles.

Step4: Check mid - point of a segment for O

Since $\overline{NO}\cong\overline{OK}$, O is the mid - point of segment $\overline{NK}$.

Step5: Check mid - point of a segment for P

There is no information to suggest that P is the mid - point of a segment.

Answer:

O is the midpoint of a segment in the diagram.