Question

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

Explanation:

Step1: Recall the property of perpendicular bisector

If a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Here, line \(l\) is the perpendicular bisector of segment \(RT\) (since \(X\) is the mid - point of \(RT\) and \(SX\perp RT\)).

Step2: Apply the perpendicular bisector theorem

By the perpendicular bisector theorem, \(SR = ST\)

Answer:

\(\overline{SR}\)