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proof- In ΔPQR, QR is produced to S
so,∠PRS = ∠QPR + ∠PQR (EXTERIOR ANGLE PROPERTY)
1/2 ∠PRS = 1/2∠QPR + 1/2∠PQR
∠TRS = 1/2 ∠QPR + ∠TQR - (1) <QT and RT are the angle bisector of∠PQR and ∠PRS respectively >
In ΔTQR, QR is produced to S
∠TRS = ∠QTR + ∠TQR -(2)
From equation (1) & (2)
1/2 ∠QPR + ∠TQR = ∠QTR + ∠TQR
Hence, ∠QTR = 1/2 ∠QPR (PROVED)
so,∠PRS = ∠QPR + ∠PQR (EXTERIOR ANGLE PROPERTY)
1/2 ∠PRS = 1/2∠QPR + 1/2∠PQR
∠TRS = 1/2 ∠QPR + ∠TQR - (1) <QT and RT are the angle bisector of∠PQR and ∠PRS respectively >
In ΔTQR, QR is produced to S
∠TRS = ∠QTR + ∠TQR -(2)
From equation (1) & (2)
1/2 ∠QPR + ∠TQR = ∠QTR + ∠TQR
Hence, ∠QTR = 1/2 ∠QPR (PROVED)
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