In the figure given below the side QR of Triangle PQR is produced to a point S. If the bisectors of ∠ PQR and ∠ PRS meet at point T, then prove that ∠ QTR = ½ ∠ QPR
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1
Answer:
Step-by-step explanation:
Given, Bisectors of ∠PQRand ∠PRS meet at point T.
To prove: ∠QTR=
2
1
∠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
⇒
2
1
∠QPR=∠TRS−∠TQR --- (ii)
Equating (i) and (ii),
∴∠QTR=
2
1
∠QPR [henceproved]
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Answer:
Step-by-step explanation:
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