Question

prove that an isosceles trapezium is a cyclic quadrilateral

Answer 1

let the trapezium be ABCD with AB ll CD
then angleA = angleB
angleC = angleD
By ASP of quadrilateral
angleA + angleB + angleC + angleD = 360°
from above
angleA + angleA + angleC + angleC = 360°
2(angleA + angleC)=360°
angleA + angleC = 180°
similarly,
angleB + angleD = 180°

since sum of opposite angle is 180° therefore it is a cyclic Quadrilateral

Answer 2

Answer:

OPPOSITE ANGLES OF A CYCLIC QUADRILATERAL ARE SUPPLEMENTRY

Hence Proved

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