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in the adjoining quadrilateral ABCD, AO and BO are the bisector of angle A and angle B respectively Prove that Angle AOB = 1/2 ( angle C + angle D ) |
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Answer» ABCD is a quadrilateralTo PROVE : ∠AOB= 21 (∠C+∠D)AO and BO is BISECTOR of A and B ∠1=∠2∠3=∠4...(1)∠A+∠B+∠C+∠D=360(Angle SUM property)21 (∠A+∠B+∠C+∠D)=180...(2)In △AOB∠1+∠3+∠5= 21 (∠A+∠B+∠C+∠D)∠1+∠3+∠5=∠1+∠3+ 21 (∠C+∠D)∠AOB= 21 (∠C+∠D) |
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