Question

POQ is a straight line. OT bisects angle POR and OS bisects angle QOR.Show that angle SOT is a right angle triangle

Answer 1

Given - <POQ is a straight line ,

OT bisects <POR , OS bisects <QOR

To proof : <SOT is a right angle

Proof :

POQ is a straight line , & OT bisects <POR ,

so <POT = <TOR --(1)

POQ is a st. line and OS bisects <QOR ,

SO

<ROS = <SOQ --(2)

since

OR stands on POQ

then ,<POR+<ROQ = 180 degree

<POT+<TOR+<ROS+<SOQ= 180 degree <TOR+<TOR+<ROS+<ROS=180 degree

----(from 1&2)

= 2(<TOR+<ROS) = 180 degree

= .<TOR+<ROS = 180/2

= <TOR+,ROS = 90 degree

therefore <SOT = 90 degree

Hence proved.

Answer 2

heya..

here is your answer..

Given - <POQ is a straight line , OT bisects <POR , OS bisects <QOR                            To proof : <SOT is a right angle                                                                                          Proof : POQ is a straight line , & OT bisects <POR , so <POT = <TOR --(1)                     POQ is a st. line and OS bisects <QOR , SO <ROS = <SOQ --(2)                                since OR stands on POQ then ,<POR+<ROQ = 180 degree                                  <POT+<TOR+<ROS+<SOQ= 180 degree                                                                  <TOR+<TOR+<ROS+<ROS=180 degree ----(from 1&2)                                                = 2(<TOR+<ROS) = 180 degree                                                                                        <TOR+<ROS = 180/2                                                                                                         <TOR+,ROS = 90 degree                                                                                                    therefore <SOT = 90 degree                                                                                               Hence proved.

it may help you..☺️☺️