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:

Step1: Analyze segment - bisector property

There is no indication that $\overline{PQ}$ divides another segment into two equal - length parts, so $\overline{PQ}$ is not a segment bisector.

Step2: Analyze angle - congruence at point Q

Since $OQ = QN$ and we assume some parallel - line or congruence - related properties (if this is part of a larger geometric figure context like a parallelogram - related setup), $Q$ can be the vertex of two congruent angles. For example, if $OP\parallel QM$, then alternate - interior angles or vertical angles involving $Q$ can be congruent.

Step3: Analyze right - angle at point P

There is no information in the diagram to suggest that $\angle{OPQ}$ or $\angle{MPQ}$ is a right angle.

Step4: Analyze right - angle at point Q

There is no information in the diagram to suggest that any angle with vertex $Q$ is a right angle.

Step5: Analyze mid - point property of Q

From the diagram, we can see that $Q$ is the mid - point of segment $\overline{ON}$ as $OQ = QN$.

Answer:

Q is the vertex of two angles that are congruent to one another, Q is the midpoint of a segment in the diagram.