Question

Prove that angles inscribed in the same arc are congruent.

Given: In a circle with center C, ∠PQR and ∠PSR are inscribed in same arc PQR. Arc PTR is intercepted by the angles.

To prove: ∠PQR ≅ ∠PSR.

Proof:

`m∠PQR = 1/2 xx [m(arc  PTR)]`   ...(i) `square`

m∠`square` = `1/2 xx [m(arc  PTR)]`   ...(ii) `square`

m∠`square` = m∠PSR   ...[By (i) and (ii)]

∴ ∠PQR ≅ ∠PSR

Answer 1

Given: In a circle with center C, ∠PQR and ∠PSR are inscribed in same arc PQR. Arc PTR is intercepted by the angles.

To prove: ∠PQR ≅ ∠PSR.

Proof:

`m∠PQR = 1/2 xx [m(arc  PTR)]`   ...(i) \[\boxed{\text{Inscribed angle theorem}}\]

m∠\[\boxed{PSR}\] = `1/2 xx [m(arc  PTR)]`   ...(ii) \[\boxed{\text{Inscribed angle theorem}}\]

m∠\[\boxed{\text{PQR}}\] = m∠PSR   ...[By (i) and (ii)]

∴ ∠PQR ≅ ∠PSR