In the figure ,POQ is aline. Ray OR is perpendicular to line. OS is a ray lying b/w OP & OR. PROVE THAT <ROS = 1/2[<QOS - <POS]
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☺ Hello mate__ ❤
◾◾here is your answer...
Given: OR is perpendicular to PQ
OR and OS are rays to PQ
To prove: ∠ROS=1/2(∠QOS−∠POS)
Proof: ∠ROQ+∠ROP=180° (Linear pair)
⇒∠ROP=180°−∠ROQ=180°−90°=90°
R.H.S =1/2(∠QOS−∠POS)
=1/2(180°−∠POS−∠POS) (∠POS+∠QOS=180°) (Linear pair)
=1/2(180°−2∠POS) ...........eq (1)
We have ∠POS=∠ROP−∠ROS=90°−∠ROS, putting this in eq(1), we get
R.H.S =1/2(180°−2(90°−∠ROS))
=1/2(180°−180°+2∠ROS)=1/2(2∠ROS)
=∠ROS
Therefore, L.H.S=R.H.S
Hence proved.
I hope, this will help you.
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