Question

The side QR of a triangle PQR is produced to a point S. If the bisector of
ZPQR and < PRS meet at point T, QPR (See given Figure), then prove that;
LQTR =ZQPR
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Answer 1

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Answer 2

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Class 7

>>Maths

>>The Triangle and Its Properties

>>Exterior Angle of a Triangle

>>In Figure, the side QR of PQR is produc

Question



In Figure, the side QR of △PQR is produced to a point S. If the bisectors of ∠PQR and ∠PRS meet at point T, then prove that ∠QTR=21∠QPR.





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Solution



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Given, Bisectors of ∠PQRand ∠PRS meet at point T.

To prove: ∠QTR=21∠QPR.

Proof,

∠TRS=∠TQR+∠QTR (Exterior angle of a triangle equals to the sum of the two interior angles.)

⇒∠QTR=∠TRS−∠TQR --- (i)

Also ∠SRP=∠QPR+∠PQR

2∠TRS=∠QPR+2∠TQR

∠QPR=2∠TRS−2∠TQR 

⇒21∠QPR=∠TRS−∠TQR --- (ii)

Equating (i) and (ii),

∴∠QTR=21∠QPR   [henceproved]