6. In Fig. 6.44, the side QR of \Delta PQR is produced to a point S. If the bisectors of \angle PQR and \angle PRS meet at point T, then prove that  \angle QTR = \frac{1}{2}   \angleQPR.

                

Answers (1)


We have, 
\Delta PQR is produced to a point S and  bisectors of \angle PQR and \angle PRS meet at point T,
By exterior angle sum property,
\angle PRS = \angleP + \anglePQR
Now, \frac{1}{2}\angle PRS =\frac{1}{2}\angle P + \frac{1}{2} \angle PQR
\Rightarrow \angle TRS = \frac{1}{2}\angle P + \angle TQR................(i)

Since QT and QR are the bisectors of  \angle PQR and \angle PRS respectively.

Now, in \DeltaQRT,
\angle TRS = \angle T + \angle TQR..............(ii)

From eq (i) and eq (ii),  we get

\frac{1}{2}\angle P= \angle T
\Rightarrow \frac{1}{2}\angle QPR= \angle QTR
Hence proved

Preparation Products

JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Rank Booster NEET 2021

This course will help student to be better prepared and study in the right direction for NEET..

₹ 13999/- ₹ 9999/-
Buy Now
Knockout JEE Main April 2021 (Easy Installments)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 4999/-
Buy Now
Knockout NEET May 2021

An exhaustive E-learning program for the complete preparation of NEET..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout NEET May 2022

An exhaustive E-learning program for the complete preparation of NEET..

₹ 34999/- ₹ 24999/-
Buy Now
Exams
Articles
Questions