Question

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

Answer 1

Answer:

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

Answer 2

Answer:

b

Step-by-step explanation:

just took the test