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Prove that, angles inscribed in the same...

Prove that, angles inscribed in the same arc are congruent
`/_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 ) ` …...`square`
`m /_ square = (1)/(2) m (arc PXR )` ....(2) `square `
`:. m /_ square = m /_ PSR ` ......[ From (1) and (2) ]
`:. /_PQR ~= /_ PSR ` ...(Angles equal in measure are congrument )

Text Solution

Verified by Experts

`m/_PQR = (1)/( m ) (arc PXR ) ` ….(1) Inscribed angle theorem
`m /_ PSR = (1)/(2) m ( arc PXR ) ` ….(2) Inscribed angle theorem
`:. M /_PQR = m /_PSR ` ….[From (1) and (2) ]
`:. /_PQR ~= /_PSR ` ….(Angles equal in measure are congruent)
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