Question

Prove the following theorem:

Angles inscribed in the same arc are congruent.

Answer 1

Given: C is the circle's center. In the same arc PTR, ∠PQR and ∠PSR are written.

To prove: ∠PQR ≅ ∠PSR

Proof:

arc PTR is intercepted by ∠PQR.

arc PTR is intercepted by ∠PSR.

`∠PQR = 1/2 m(arc  PTR)`   ...(i) [Inscribed angle theorem]

And 

`∠PSR = 1/2 m(arc  PTR)`   ...(ii) [Inscribed angle theorem]

∴ ∠PQR ≅ ∠PSR   ...[From (i) and (ii)]