Question

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 $overline{ps}$

Explanation:

Step1: Recall the vertical - angle and chord relationship

In a circle, if two central angles (or inscribed angles subtended by the same arc) are congruent, the chords they subtend are congruent. Since angles PTQ and STR are vertical angles and congruent, and they subtend chords QP and SR respectively.

Step2: Identify the congruent chords

Based on the above - mentioned property, chords QP and SR are congruent.

Answer:

QP and SR