# Angles inscribed in the same arc are congruent. Write ‘given’ and ‘to prove’ with the help of the given figure.

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ago in Circle
edited ago

Angles inscribed in the same arc are congruent.

Write ‘given’ and ‘to prove’ with the help of the given figure.

Think of the answers of the following questions and write the proof.

i. Which arc is intercepted by ∠PQR ?

ii. Which arc is intercepted by ∠PSR ?

iii. What is the relation between an inscribed angle and the arc intercepted by it?

ago by (35.1k points)
edited ago by

Given: C is the centre of circle. ∠PQR and ∠PSR are inscribed in same arc PTR.

To prove: ∠PQR ≅ ∠PSR

Proof:

i. arc PTR is intercepted by ∠PQR.

ii. arc PTR is intercepted by ∠PSR.

iii. ∠PQR = 1/2 m(arc PTR), and (i) [inscribed angle theorem]

∠PSR = 1/2 m(arcPTR) (ii) [Inscribed angle theorem]

∴ ∠PQR ≅ ∠PSR [From (i) and (ii)]