Question

3. ABCD is a trapezium with AB II DC. A line parallel to AC intersects AB at X and BC
at Y. Prove that ar (ADX) = ar (ACY).
A
(Hint: Join CX with diagram

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Answer 1

Answer:

Hope the above attachment help you..

Answer 2

Answer:

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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)

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