Question

Angles PTQ and STR are vertical angles and congruent. which arcs are congruent

Answer 1

Answer: I believe the answer is arc PQ and SR are congruent

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

PQ≈SR

Answer 2

Answer:

arc PQ and arc SR are congruent. arc PS and arc QR are congruent

Step-by-step explanation:

since you didn't give me a graph, im assuming its a circle. The circle is intersected by two chords, with end point PQRS in this order. Use circle properties.