Angles ptq and str are vertical angles and congruent.

circle t is shown. line segments t p, t q, t r, and t s are radii. lines are drawn to connect points p and q and points s and r to create secants. angles p t q and r t s are congruent.

which arcs are congruent?

arc s p and arc s r
arc p q and arc s r
arc p q and arc q r
arc s p and arc p r

Step-by-step explanation:

Chords QP and RS are congruent

Chords PS and QR are congruent

Step-by-step explanation:

see the attached figure to better understand the problem

Part 1)

we know that

m∠PTQ≅m∠STR > by vertical angles

so

Triangles PTQ and STR are congruent by SAS postulate

because

PT≅ST > the radius of circle

QT≅RT > the radius of circle

m∠PTQ≅m∠STR

therefore

Chords QP and RS are congruent

Part 2)

we know that

m∠PTS≅m∠QTR > by vertical angles

so

Triangles PTS and QTR are congruent by SAS postulate  

because

PT≅QT > the radius of circle

ST≅RT > the radius of circle

m∠PTS≅m∠QTR

therefore

Chords PS and QR are congruent

i can you with this question sweetie!

step-by-step explanation: