Question
Prove that angles inscribed in the same arc are congruent.
Given: In a circle with center $C, \angle P Q R$ and $\angle P S R$ are inscribed in same arc PQR. Arc PTR is intercepted by the angles.
To prove: $\angle P Q R \cong \angle P S R$.
Proof:
$ m \angle PQR =\frac{1}{2} \times[ m (\operatorname{arc} PTR )]$
$m \angle \square=\frac{1}{2} \times[ m (\operatorname{arc} PTR )] \ldots . . . \text { (ii) } \square$
$m \angle \square= m \angle PSR \quad \ldots . . .[ By \text { (i) and (ii) }]$
$\therefore \angle PQR \cong \angle PSR $
Given: In a circle with center $C, \angle P Q R$ and $\angle P S R$ are inscribed in same arc PQR. Arc PTR is intercepted by the angles.
To prove: $\angle P Q R \cong \angle P S R$.
Proof:
$ m \angle PQR =\frac{1}{2} \times[ m (\operatorname{arc} PTR )]$
$m \angle \square=\frac{1}{2} \times[ m (\operatorname{arc} PTR )] \ldots . . . \text { (ii) } \square$
$m \angle \square= m \angle PSR \quad \ldots . . .[ By \text { (i) and (ii) }]$
$\therefore \angle PQR \cong \angle PSR $
