Question

in circle q, ∠rqs≅∠sqt. which statement must be true? rs≅st ∠rqt≅∠rst rq⊥qt rt≅ut

Explanation:

Step1: Recall circle - angle and arc relationship

In a circle, if two central angles are congruent, then the arcs they intercept are congruent. Since \(\angle RQS\cong\angle SQT\), and \(\angle RQS\) intercepts arc \(\overset{\frown}{RS}\) and \(\angle SQT\) intercepts arc \(\overset{\frown}{ST}\).

Step2: Determine the congruent arcs

By the central - angle theorem, we can conclude that \(\overset{\frown}{RS}\cong\overset{\frown}{ST}\).

Answer:

\(\overset{\frown}{RS}\cong\overset{\frown}{ST}\)