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
$overline{uv}$ is a segment bisector.
$overline{uv}$ is a perpendicular bisector.
$overline{uv}$ is an angle bisector.
$v$ is the vertex of a right angle.
$v$ is the midpoint of a segment in the diagram.
none of the above.

Explanation:

1. A segment bisector divides a segment into two equal parts. The marks show $RU=US$ and $RV=VQ$, so $\overline{UV}$ splits both $\overline{RS}$ and $\overline{RQ}$ into congruent segments, making it a segment bisector.
2. There is no indication of right angles, so $\overline{UV}$ cannot be a perpendicular bisector, and $V$ is not the vertex of a right angle.
3. $\overline{UV}$ does not split any angle shown into two equal angles, so it is not an angle bisector.
4. $V$ is the midpoint of $\overline{RQ}$, which is a segment in the diagram.

Answer:

$\overline{UV}$ is a segment bisector.
$V$ is the midpoint of a segment in the diagram.