Question

T
P
6.) in Fig. 6.44, the side QR of APQR is produced to
a point S. If the bisectors of Z PQR and
PRS meet at point T, then prove that
1
LQTR= = ZQPR.
R
S
Fig. 6.44
68 Summary​

Answer 1

Step-by-step explanation:

Concept to be used: The exterior angle of a triangle is equal to the sum of two interior opposite angles of the triangle

Considering the exterior angle of ΔTQR, we have

∠TRS = ∠TQR + ∠QTR

⇒ ∠QTR = ∠TRS - ∠TQR ....... (i)

Considering the exterior angle of Δ PQR, we have

∠PRS = ∠PQR + ∠QPR

[∵ QT is the bisector of ∠PQR & TR is the bisector of ∠PRS (as shown in the fig)]

⇒ 2∠TRS = 2∠TQR + ∠QPR

⇒ ∠QPR = 2∠TRS - 2∠TQR

⇒ ∠QPR = 2[∠TRS - ∠TQR]

⇒ ∠TRS - ∠TQR = \frac{1}{2}

2

1

∠QPR ....... (ii)

Now, on comparing (i) & (ii), we get

\boxed{\boxed{\underline{\bold{\angle QTR = \frac{1}{2}\angle QPR }}}}

∠QTR=

2

1

∠QPR

Hence proved

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