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+1 vote
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in Mathematics by (15.0k points)

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).

1 Answer

+1 vote
by (24.9k points)
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Best answer

It is given that OR ⊥ PQ

POR = 90º

POS + SOR = 90º

ROS = 90º − POS … (1)

QOR = 90º (As OR  PQ)

QOS − ROS = 90º

ROS = QOS − 90º … (2)

On adding equations (1) and (2), we obtain

ROS = QOS − POS

ROS = 1/2(QOS − POS)

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