Question

please help me out
please​

Answer 1

given,

POQ is a line

Ray OR is perpendicular to line PQ

OS is another ray lying between rays OP and OR

To prove,

ROS = 1\2 (QOS-POS)

solution,

In POR,

POR = POS + ROS. _______ (i)

In QOS,

QOS = QOR + ROS

QOR = QOS - ROS. _______ (ii)

Ray OR is perpendicular to line PQ ( given )

So,

QOR = POR

In equation (i) and (ii)

POS + ROS = QOS - ROS

2 ROS = QOS - POS

ROS = 1\2 ( QOS - POS )

proved.