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In Fig. 6.44, the side QR of PQR is pr...

In Fig. 6.44, the side QR of PQR is produced to a point S. If the bisectors of `/_P Q R` and `/_P R S` meet at point T, then prove that `/_Q T R=1/2/_Q P R`.

Text Solution

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`In/_ PQR`
`anglePRS=anglePQR+angleQPR`(exterior angle of triangle)
`1/2 anglePRS=1/2anglePQR+1/2angleQPR`
`angleTRS=angleTQS+1/2angleQPR-(1)`
`In/_QTS`
`angleTRS=angleTQR+angleQTR-(2)`
`angleTQS+angleQTR=angleTQS+1/2angleQPR`
`angleQTR=1/2angleQPR`
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