[tex] \text{PROVE:}\ \angle ROS=\dfrac{1}{2}(\angle QOS-\angle POS)\\\\\angle QOR=90^o\\\angle QOS=90^o+\angle ROS\\\angle POS=90^o-\angle ROS\\\\\text{substitute}\\\\\angle ROS=\dfrac{1}{2}[90^o+\angle ROS-(90^o-\angle ROS)]\\\angle ROS=\dfrac{1}{2}(90^o+\angle ROS-90^o+\angle ROS)\\\angle ROS=\dfrac{1}{2}(2\angle ROS)\\\angle ROS=\angle ROS [/tex]
