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)]