Question

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 .Prove that
<ROS=½(<QOS -<POS)
​

Answer 1

Solution

To prove : ∠ROS = 1/2(∠QOS - ∠POS)

∵ OR ⊥ PQ

∠ROP = 90°

And ∠ROQ = 90°

Now,

We can say that

∠ROP = ∠ROQ

⇒∠POS + ∠ROS = ∠ROQ

⇒ ∠POS + ∠ROS = ∠QOS - ∠ROS

⇒∠ROS + ∠ROS = ∠QOS - ∠POS

⇒2∠ROS = ∠QOS - ∠POS

⇒∠ROS = 1/2(∠QOS - ∠POS)

Hence, proved