angles ptq and str are vertical angles and congruent. which chords are congruent? o $overline{qp}$ and…

angles ptq and str are vertical angles and congruent. which chords are congruent? o $overline{qp}$ and $overline{sr}$ o $overline{qr}$ and $overline{pq}$ o $overline{pr}$ and $overline{rs}$ o $overline{pr}$ and $overline{ps}$

angles ptq and str are vertical angles and congruent. which chords are congruent? o $overline{qp}$ and $overline{sr}$ o $overline{qr}$ and $overline{pq}$ o $overline{pr}$ and $overline{rs}$ o $overline{pr}$ and $overline{ps}$

Answer

Explanation:

Step1: Recall the property of vertical - angles in a circle

Vertical angles in a circle subtend congruent arcs. Since (\angle PTQ) and (\angle STR) are vertical angles and congruent, the arcs they subtend are congruent. The arc subtended by (\angle PTQ) is (\overset{\frown}{PQ}) and the arc subtended by (\angle STR) is (\overset{\frown}{SR}).

Step2: Recall the relationship between arcs and chords

In a circle, congruent arcs have congruent chords. Since (\overset{\frown}{PQ}\cong\overset{\frown}{SR}), then the chords that subtend these arcs are congruent. The chord that subtends (\overset{\frown}{PQ}) is (\overline{PQ}) and the chord that subtends (\overset{\frown}{SR}) is (\overline{SR}).

Answer:

(\overline{QP}) and (\overline{SR})