Question

which of the following statements must be true based on the diagram below? select all that apply. (diagram is not shown completely in the ocr but we have the text part). answer attempt 1 out of 2
\\(\overline{tx}\\) is a segment bisector.
\\(\overline{tx}\\) is a perpendicular bisector.
\\(\overline{tx}\\) is an angle bisector.
\\(t\\) is the vertex of a right angle.
\\(t\\) 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 at a right - angle. Angle bisector divides an angle into two equal - measure angles.

Step2: Analyze the diagram

The marks on the angles at $\angle WTX$ and $\angle XTU$ indicate that $\overline{TX}$ divides $\angle WTU$ into two equal - measure angles. So, $\overline{TX}$ is an angle bisector. There is no indication that $\overline{TX}$ bisects a segment (neither as a segment bisector nor a perpendicular bisector), there is no right - angle at $T$ shown, and $T$ is not shown as a mid - point of any segment.

Answer:

$\overline{TX}$ is an angle bisector.