Question

ABCD is a trapezium with AB||DC.A line parallel to AC intersectAB at X and BC at Y. Prove that ar( ADX)=ar(ACY).​

Answer 1

Answer:

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Step-by-step explanation:

Given : ABCD is a trapezium with AB∥DC and XY∥AC.

Join YA,XC and XD.

Triangles ACX and ACY have same base AC and are between same parallels AC and XY

So, ar(△ACX)=ar(△ACY) ......(i)

Triangles ACX and ADX have same base AX and are between same parallels AB and DC.

So, ar(△ACX)=ar(△ADX) ......(ii)

From (i) and (ii),

ar(△ADX)=ar(△ACY)