Question

what is rs?
rs =
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not feeling ready yet? these can help:
solve linear equations: mixed review
congruent line segme
parallel, perpendicular, and intersecting lines
lesson: perpendicula

Explanation:

Step1: Identify the perpendicular bisector

The line \( RT \) is perpendicular (\( \angle RTS = 90^\circ \)) and bisects \( SQ \) (since the segments are marked congruent), so \( RT \) is the perpendicular bisector of \( SQ \).

Step2: Apply the perpendicular bisector theorem

By the perpendicular bisector theorem, any point on the perpendicular bisector is equidistant from the endpoints of the segment. So \( RS = RQ \).

Step3: Determine the length of \( RS \)

Given \( RQ = 51 \), so \( RS = RQ = 51 \).

Answer:

\( 51 \)