Q8 of 45 Page 43

From the information given in the figure 2.31, prove that PM = PN =


In ΔPQS and ΔPSR, By Pythagoras theorem


i.e. (Hypotenuse)2 = (base)2 + (Perpendicular)2


PQ2 = QS2 + PS2 [1]


PR2 = SR2 + PS2 [2]


Subtracting [2] from [1],


PQ2 - PR2 = QS2 - SR2


⇒ a2 - a2 = QS2 - SR2


⇒ QS2 = SR2


⇒ QS = SR



Also,


MS = MQ + QS



And


SN = SR + RN



In ΔPSM and ΔPSN, By Pythagoras theorem


PM2= PS2 + MS2


[3]


PN2= PS2 + SN2


[4]


From [3] and [4]


PM2 = PN2


⇒ PM = PN


Hence Proved.


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