Question

which of the following statements must be true based on the diagram below? select all that apply. (diagram is not to scale.) uy is a segment bisector. uy is a perpendicular bisector. uy is an angle bisector. u is the vertex of two angles that are congruent to one another. u is the midpoint of a segment in the diagram. none of the above.

Explanation:

Step1: Recall definitions

Segment - bisector divides a segment into two equal - length segments. Perpendicular bisector divides a segment into two equal - length segments and is perpendicular to it. Angle - bisector divides an angle into two equal - measure angles.

Step2: Analyze the diagram

Since there are no markings indicating perpendicularity or equal - angles, we can't say $UY$ is a perpendicular bisector or an angle bisector. But since the line $UY$ intersects the segment $VW$ at its mid - point (assumed from the equal - length markings on $VW$), $UY$ is a segment bisector. Also, $\angle VUY$ and $\angle WUY$ are two angles with vertex $U$ and there is no information to suggest they are congruent. And there is no indication that $U$ is the mid - point of any segment.

Answer:

$UY$ is a segment bisector.