Question

in the diagram, $overline{tq}$ is 18 units in length. what is the length of $overline{rs}$? 16 units 18 units 25 units 46 units

Explanation:

Step1: Identify congruent segments

The line \(l\) is a perpendicular - bisector of \(\overline{RQ}\). So, \(\overline{RT}=\overline{TQ}\) and \(\overline{RS}=\overline{SQ}\).
Since \(\overline{TQ} = 18\) units and \(\overline{RT}=\overline{TQ}\), and \(\triangle RTS\cong\triangle QTS\) (by Side - Angle - Side (SAS) congruence criterion as \(RT = TQ\), \(\angle RTS=\angle QTS = 90^{\circ}\), and \(TS\) is common).
So, \(\overline{RS}=\overline{SQ}\). Also, because of the properties of the perpendicular bisector, \(\overline{RS}=\overline{TQ}=18\) units.

Answer:

18 units