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6 In the Fig. given below, LQ > ZR, PA is the bisector of LQPR and PM 1 QR. Prove thatZAPM = (ZQ - _R).RM |
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Answer»
ANSWER In△PAQ Sumoftwooppositeinteriorangles=Exteriorangle α=θ+∠θ−(i) In△PAR α+θ+∠R=180 ∘
α=180 ∘ −θ−∠R−(II) In△PMQ ∠MPQ=180−∠Q−90 ∘
=90−∠Q ∠APM=∠APQ−∠MPQ =θ−(90−∠Q) =θ+∠Q−90 ∘ −(III) ∵(i)=(ii) =>θ+∠Q=180−θ−∠R =>2θ=180−∠Q−∠R =>θ=90− 2 1
(∠Q+∠R) puttingthisvalueofθin(iii) ∠APM=∠Q+90− 2 1
(∠Q+∠R)−90 = 2 ∠Q
− 2 ∠R
= 2 1
(∠Q−∠R) ∴a=2
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