In angle XYZ,A and B are points on sides XZ and YZ respectively YA and XB intersect at O If - Maths - Areas of Parallelograms and Triangles

Question

In angle XYZ,A and B are points on sides XZ and YZ respectively YA
and XB intersect at O If AB parallel XY,than show that ar(angle
AOX)=ar(angle BOY)

Anuradha Sharma · Accepted Answer

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We know that ∆'s having same base and between same parallels are equal in area
Since XY||AB and triangle XAB and ABY are on same base AB and between same parallels AB and XYSo, Area of ∆XAB= Area of ∆ ABYNow subtracting area of ∆ OAB both side , we get Area of ∆ XAB-area of ∆ OAB= Area of ∆ ABY-area of ∆ OABArea of ∆ OAX= Area of ∆OBY

In angle XYZ,A and B are points on sides XZ and YZ respectively.YA and XB intersect at O.If AB parallel XY,than show that ar(angle AOX)=ar(angle BOY).