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

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Akshita Viswan
From Gems Our Own Indian School, added an answer, on 17/12/11

326 helpful votes in Math
In the fig. ABCD is a trapezium with AB II DC.. nd

COnstruction- Draw AC (digonal) . Draw a line XY parallel to AC in which X intersects at AB nd Y intersects at BC

__ COnsider triangle ADX nd triangle ACX __

since these triangles share a common base AX nd lie between same parallels AB nd DC..

ar(ADX) = ar(ACX) ---- 1

__ Consider triangle ACX nd triangle ACY __

since dese triangles share common base AX and lie between same parallels AC nd XY

ar(ACX)= ar(ACY) --- 2

From 1 and 2

__ ar(ADX) = ar(ACY) __

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