Question

which of the following statements must be true based on the diagram below? select all that apply. (diagram is not to scale.)

answer
$overline{pq}$ is a segment bisector.
$q$ is the vertex of two angles that are congruent to one another.
$p$ is the vertex of a right angle.
$q$ is the vertex of a right angle.
$q$ is the midpoint of a segment in the diagram.
none of the above.

Explanation:

1. $\overline{PQ}$ is a segment bisector: A segment bisector divides a segment into two equal parts. The diagram shows $Q$ splits $\overline{ON}$ into two congruent segments, so $\overline{PQ}$ bisects $\overline{ON}$. This is true.
2. $Q$ is the vertex of two congruent angles: There is no marking or given information to confirm angles at $Q$ are congruent. This is not necessarily true.
3. $P$ is the vertex of a right angle: No right angle symbol or info confirms this. Not necessarily true.
4. $Q$ is the vertex of a right angle: No right angle symbol or info confirms this. Not necessarily true.
5. $Q$ is the midpoint of a segment in the diagram: The markings show $Q$ splits $\overline{ON}$ into two equal parts, so $Q$ is the midpoint of $\overline{ON}$. This is true.

Answer:

$\overline{PQ}$ is a segment bisector.
$Q$ is the midpoint of a segment in the diagram.