Q. 73.6( 24 Votes )

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


Answer :

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]


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