Question

consider the diagram. which line segment has the same measure as \\( \overline{tq} \\)? \\( \overline{sr} \\) \\( \overline{tr} \\) \\( \overline{st} \\) \\( \overline{qs} \\)

Explanation:

Step1: Recall the property of perpendicular bisector

A perpendicular bisector of a line segment divides the line segment into two equal parts. Also, any point on the perpendicular bisector is equidistant from the endpoints of the line segment.
In the given diagram, line \(m\) is the perpendicular bisector of \(QR\).

Step2: Apply the equidistant property

Since \(T\) lies on the perpendicular bisector \(m\) of \(QR\), by the perpendicular bisector theorem, \(TQ = TR\).

Answer:

\(\overline{TR}\)