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
$overline{vu}$ is a segment bisector.
$overline{vu}$ is a perpendicular bisector.
$v$ is the vertex of a right angle.
$u$ 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. $\overline{VU}$ splits $\overline{ST}$ into two marked equal segments, so it is a segment bisector.
2. A perpendicular bisector is a segment bisector that is also perpendicular to the segment. $\overline{VU}$ forms a right angle with $\overline{ST}$ (marked by the square symbol) and bisects it, so it is a perpendicular bisector.
3. The right angle symbol is at point $V$, so $V$ is the vertex of the right angle.
4. Point $V$ divides $\overline{ST}$ into two equal parts, so $V$ is the midpoint of $\overline{ST}$.
5. The right angle is at $V$, not $U$, so the statement about $U$ being the right angle vertex is false.

Answer:

$\overline{VU}$ is a segment bisector.
$\overline{VU}$ is a perpendicular bisector.
$V$ is the vertex of a right angle.
$V$ is the midpoint of a segment in the diagram.