Question

if (overline{rs}congoverline{st}) and (ru = 54), what is (rt)?

Explanation:

Step1: Use the perpendicular bisector theorem

Since \(RS\cong ST\) and \(SU\perp RT\), by the perpendicular bisector theorem (if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment), \(SU\) is the perpendicular bisector of \(RT\). So \(RU = UT\).

Step2: Calculate \(RT\)

We know that \(RT=RU + UT\). Given \(RU = 54\) and \(RU=UT\), then \(RT=54 + 54\).

Answer:

\(108\)