Question

consider the diagram
which line segment has the same measure as \\( \overline { st } \\)?
\\( \overline { tx } \\)
\\( \overline { rx } \\)
\\( \overline { xs } \\)
\\( \overline { sr } \\)

Explanation:

Step1: Recall the property of perpendicular bisector

A perpendicular bisector of a line segment divides the line segment into two equal parts and is perpendicular to it. Also, any point on the perpendicular bisector is equidistant from the endpoints of the line segment.

Step2: Analyze the given diagram

In the diagram, the line passing through \(X\) is the perpendicular bisector of \(RT\). Point \(S\) lies on this perpendicular bisector. So, by the property of the perpendicular bisector, \(SR = ST\).

Answer:

\(\overline{SR}\)