Question

In the figure, POQ is a straight line. OA and OB are bisectors of ZPOR and ZQOR respectively. Show that ZAOB is a right angle. A B P Q​

Answer 1

In the figure, POQ is a straight line. OA and OB are bisectors of ZPOR and ZQOR respectively. Show that ZAOB is a right angle. A B P Q

Answer 2

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.

Step-by-step explanation: