Question

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

Explanation:

Step1: Analyze the properties of the perpendicular bisector

Since line \(m\) is the perpendicular bisector of \(QR\), any point on line \(m\) is equidistant from \(Q\) and \(R\).

Step2: Apply the property to points \(T\)

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

Answer:

\(\overline{TR}\)