Question

Prove that, angles inscribed in the same arc are congruent. 

Given: ∠PQR and ∠PSR are inscribed in the same arc

Arc PXR is intercepted by the angles. 

To prove: ∠PQR ≅ ∠PSR 

Proof : 

m∠PQR = `1/2` m(arc PXR)    .......(i) `square`

m∠`square` = `1/2` m(arc PXR)   ......(ii) `square`

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

∴ ∠PQR ≅  ∠PSR       ........(Angles equal in measure are congruent)  

Answer 1

Proof : 

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

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

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

∴ ∠PQR ≅  ∠PSR       ......(Angles equal in measure are congruent)