# In figure 3.62, seg PT is the bisector of ∠QPR. A line through R intersects ray QP at point S. Prove that PS = PR

Given: PT is angle bisector of QPR

QPT = RPT

A line through R parallel to PT intersects ray QP at S

RS || PT

To Prove: PS = PR

Proof:

PT is angle bisector of QPR

QPT = RPT

QPR = QPT + RPT

QPR = 2RPT (1)

RS || PT, PR is the transversal

So, RPT = PRS [Alternate interior angles] (2)

For ΔPRS RPQ is the remote exterior angle.

PSR + PRS = QPR

Substituting (1) and (2) in the above equation

RPT + PSR = 2RPT

PSR = RPT (3)

From (2) and (3)

PRS = PSR

PS = PR [Sides opposite to equal angles are equal]

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz | Mastering Triangles44 mins
RD Sharma | Important Proofs in Triangles28 mins
R.D. Sharma | Triangles33 mins
NCERT | Most Important Questions of Triangles50 mins
Quiz | Are You Master of Triangles?48 mins
NCERT | Tricks to Apply Triangle Inequalities45 mins
Triangles - Important Questions39 mins
RD Sharma | Problems on Triangles41 mins
NCERT | Triangle Inequalities47 mins
NCERT | Practice Imp. Qs. on Triangles44 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses