Question

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

Explanation:

Step1: Observe the diagram

The line \(l\) is the perpendicular - bisector of \(\overline{RT}\). A perpendicular - bisector of a line segment divides the line segment into two equal parts and is perpendicular to it.

Step2: Use the property of perpendicular - bisector

If a point \(S\) lies on the perpendicular - bisector of \(\overline{RT}\), then by the property of the perpendicular - bisector, any point on the perpendicular - bisector of a line segment is equidistant from the endpoints of the line segment. So, \(SR = ST\).

Answer:

C. \(\overline{SR}\)