Prove that the angle in a semi-circle is a right angle.

hi aktmail,

proof of this theorem:-

given:- PQ is a dimeter of a circle C (O,r) and angle PRQ is an angle in a semi circle.

to proof :- angle PRQ is a right angle ie; angle PRQ = 90⁰

proof:-  The angle subtended by an arc of a circle at its centre is twice the angle formed by the same arc at a point on the circle [NCERT THEOREM 10.8]

===> angle POQ = 2 angle PRQ.

===> 180⁰ = 2 angle PRQ  [ angle POQ is 180⁰ bcoz  POQ is a straight line] 

===>  angle PRQ = 180⁰ / 2

===> angle PRQ = 90^0.

HENCE PROOVED.

GIVE ME UR VALUABLE THUMBS UP IF MY PROOF IS RIGHT.