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
$overline{st}$ is a segment bisector. $overline{st}$ is an angle bisector. $s$ is the vertex of two angles that are congruent to one another. $s$ is the midpoint of a segment in the diagram. $t$ is the midpoint of a segment in the diagram. none of the above.

Explanation:

Step1: Analyze segment - bisector property

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

Step2: Analyze angle - bisector property

The angle at \(S\) is marked with two equal - angle markings, which means \(ST\) divides \(\angle QSR\) into two congruent angles. So, \(ST\) is an angle bisector.

Step3: Analyze vertex of congruent angles

Since \(ST\) is an angle bisector of \(\angle QSR\), \(S\) is the vertex of two congruent angles \(\angle QST\) and \(\angle RST\).

Step4: Analyze mid - point of a segment for \(S\)

There is no information to suggest that \(S\) is the mid - point of any segment in the diagram.

Step5: Analyze mid - point of a segment for \(T\)

The segment \(QR\) has equal markings on \(QT\) and \(TR\), which means \(T\) is the mid - point of segment \(QR\).

Answer:

\(\overline{ST}\) is an angle bisector.; \(S\) is the vertex of two angles that are congruent to one another.; \(T\) is the midpoint of a segment in the diagram.