Question

which of the following statements must be true based on the diagram below? select all that apply. (diagram is not to scale.) answer sw is a segment bisector. sw is an angle bisector. s is the vertex of two angles that are congruent to one another. s is the vertex of a right angle. w is the vertex of a right angle. none of the above.

Explanation:

Step1: Recall definitions

A segment - bisector divides a segment into two equal parts. An angle - bisector divides an angle into two equal parts.

Step2: Analyze the diagram

We see that \(TW = WU\) (marked by the congruence symbol on the segments \(TW\) and \(WU\)). Since \(SW\) intersects \(TU\) at \(W\) and \(TW=WU\), \(SW\) is a segment bisector of \(TU\).
There is no indication that \(SW\) divides any angle into two equal parts, so \(SW\) is not an angle - bisector. There is no information to suggest that any of the angles with vertex \(S\) are congruent or that any of the angles with vertex \(S\) is a right - angle. Also, there is no information to suggest that the angle with vertex \(W\) is a right - angle.

Answer:

\(\overline{SW}\) is a segment bisector.