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
$overline{uy}$ is a segment bisector. $overline{uy}$ is a perpendicular bisector. $overline{uy}$ is an angle bisector. $u$ is the vertex of two angles that are congruent to one another. $u$ is the mid - point of a segment in the diagram. none of the above.

Explanation:

Step1: Analyze segment - bisector property

Since $Y$ divides $\overline{VW}$ into two equal - length segments (the tick marks indicate $VY = YW$), $\overline{UY}$ is a segment bisector.

Step2: Analyze perpendicular - bisector property

There is no indication (no right - angle symbol) that $\overline{UY}$ is perpendicular to $\overline{VW}$, so it is not a perpendicular bisector.

Step3: Analyze angle - bisector property

There is no information to suggest that $\overline{UY}$ divides any angle at $U$ or elsewhere into two equal angles, so it is not an angle bisector.

Step4: Analyze congruent - angles property

There is no information to suggest that the angles with vertex $U$ are congruent.

Step5: Analyze mid - point property

There is no indication that $U$ is the mid - point of any segment.

Answer:

$\overline{UY}$ is a segment bisector.