Prove that ∠ ROS = 1/2 (∠ QOS – ∠ POS).
Class 9 Ncert math’s chapter 6 Lines and Angles
Page No. 97
Exercise 6.1
Question 5
In Fig. 6.17, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR.
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RHS = 1/2 (∠QOS – ∠POS)
= 1/2 [(∠QOP + ∠ROS) – (∠POR – ∠ROS)]
[∵ ∠QOS = ∠QOR + ∠ROS and ∠POS = ∠POR – ∠ROS]
= 1/2 [∠QOR + ∠ROS – ∠POR + ∠ROS]
= 1/2 [90° + ∠ROS – 90° + ∠ROS] [∵ ∠QOR = 90° and ∠POR = 90°]
= 1/2 [2∠ROS]
= ∠ROS = LHS