Question

ABCD is a trapezium with AB parallel to DC a line parallel to AC intersect AB at X and BC at Y prove that ar(ADX) = ar(ACY)

Answer 1

Given-ABCD is a trapezium
To prove-ar(ADX)=ar(ACY)
Construction-join AY,CX,,DX
Proof- in quad AXYC,
ar(ACY)=ar(AXC) -1 equation
(since they are on the same base and between the same parallels)
Now,
In quad AXCD
ar(ADX)=ar(AXC) -2 equation

From equation 1 and 2

ar(ADX)=ar(ACY) (since ar(AXC) is common therefore they get cancelled)☺

Answer 2

Hi dear..
See the attached file

I hope it will help you

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