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ABCD is a trapezium with A B\ ||\ D C. ...

ABCD is a trapezium with `A B\ ||\ D C`. A line parallel to AC intersects AB at X and BC at Y. Prove that `a r\ (A D X)\ =\ a r\ (A C Y)`.

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`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)`
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