Ex 6.1, 5 - In figure, POQ is a line. Ray OR is perpendicular - Ex 6.1

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Ex 6.1, 5 In the given figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that ∠ROS = 1/2 (∠QOS – ∠POS ) Since OR ⊥ PQ Hence, ∠ ROP = 90° & ∠ ROQ = 90° We can say that ∠ ROP = ∠ ROQ ∠ POS + ∠ ROS = ∠ ROQ ∠ POS + ∠ ROS = ∠ QOS – ∠ ROS ∠ SOR + ∠ ROS = ∠ QOS – ∠ POS 2(∠ ROS) = ∠ QOS – ∠ POS ∠ ROS = 1/2 ("∠ QOS – ∠ POS" ) ∠ ROS = 1/2 ("∠ QOS – ∠ POS" ) Hence proved

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