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4 years ago

Angles PTQ and STR are vertical angles and congruent.

Mathematics

2 answers:

ratelena [41]4 years ago

8 0

Answer: Arc SQ and Arc SR is the correct answer

lana [24]4 years ago

3 0

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

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

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

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