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{or}\\) is a segment bisector.
\\(\overline{or}\\) is a perpendicular bisector.
\\(\overline{or}\\) is an angle bisector.
\\(r\\) is the vertex of a right - angle.
\\(r\\) is the mid - point of a segment in the diagram.
none of the above.

Explanation:

Step1: Analyze segment - bisector property

There is no indication in the diagram that $\overline{OR}$ divides any segment into two equal - length parts. So, $\overline{OR}$ is not a segment bisector.

Step2: Analyze perpendicular - bisector property

There is no information suggesting that $\overline{OR}$ is perpendicular to and bisects a segment. So, $\overline{OR}$ is not a perpendicular bisector.

Step3: Analyze angle - bisector property

The angle - marking at $\angle{POR}$ and $\angle{RON}$ shows that $\overline{OR}$ divides $\angle{PON}$ into two equal angles. By the definition of an angle bisector (a ray that divides an angle into two congruent angles), $\overline{OR}$ is an angle bisector.

Step4: Analyze right - angle property

There is no right - angle symbol at any angle with $R$ as a vertex. So, $R$ is not the vertex of a right angle.

Step5: Analyze mid - point property

There is no indication that $R$ is the mid - point of any segment in the diagram.

Answer:

$\overline{OR}$ is an angle bisector.