Question

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 2 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: Analyze segment - bisector concept

There is no indication that \(TX\) divides any segment into two equal - length parts. So, \(TX\) is not a segment bisector.

Step2: Analyze perpendicular - bisector concept

There is no information to suggest that \(TX\) is perpendicular to a segment and also bisects it. So, \(TX\) is not a perpendicular bisector.

Step3: Analyze angle - bisector concept

Since the angle - bisector marks are shown at \(\angle WTX\) and \(\angle XTU\), \(\overline{TX}\) divides \(\angle WTU\) into two equal angles. So, \(\overline{TX}\) is an angle bisector.

Step4: Analyze right - angle concept

There is no right - angle mark at \(T\), so \(T\) is not the vertex of a right angle.

Step5: Analyze mid - point concept

There is no indication that \(T\) is the mid - point of any segment in the diagram.

Answer:

\(\overline{TX}\) is an angle bisector.