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Step-by-step explanation:
Here is ur answer for the third question dear..
Given,
Bisectors of angle PQR & angle PRS meet at point T.
To prove,
angleQTR=1/2 angle QPR.
Proof,
<TRS = <TQR+<QTR
exterior angle of a triangle equals to the sum of the two interior angles.
<QTR =2 <TRS - 2<TQR------------(i)
<SRP = <QPR +<PQR
2<TRS = <QPR+2 <TQR
TR is a bisector of <SRP & QT is a bisector of <PQR
<QPR=2 <TRS - 2 <TQR
<QPR =2 (<TRS - <TQR)
1/2 <QTR= TRS - <TQR -------------(ii)
Equating (i) and (ii)
<QTR=1/2 <QPR
Hence proved....
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