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.
Proove that

ROS = 1/2 ( QOS - POS)
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Answer 1

Answer:

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Answer 2

Given :-

POQ is a line.

Ray OR ⊥ Line PQ

OS is a ray which lies between Ray OP and Ray OR

To Prove :-

ROS = 1/2 (QOS - POS)

Solution :-

Given that,

(OR ⊥ PQ) and POQ = 180°

According to the question,

POS + ROS + ROQ = 180°

POS + ROS = 180°- 90° (Since POR = ROQ = 90°)

∴ POS + ROS = 90°

Now,

QOS = ROQ + ROS

Given that,

ROQ = 90°

∴ QOS = 90° + ROS

QOS - ROS = 90°

POS + ROS = 90° and QOS – ROS = 90°

Now we get,

POS + ROS = QOS - ROS

2 ROS + POS = QOS

= ROS = 1/2 (QOS - POS)

Hence Proved!