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Question
ABCD is a trapezium with AB parallel to DC. A line parallel to AC intersects AB at X and BC at Y.
Prove that the area of ∆ADX = area of ∆ACY.
Solution
Join CX, DX and AY.
Now, triangles ADX and ACX are on the same base AX and between the parallels AB and DC.
∴ A( ΔADX ) = A( ΔACX ) ….(i)
Also, triangles ACX and ACY are on the same base AC and between the parallels AC and XY.
∴ A( ΔACX ) = A( ΔACY ) ….(ii)
From (i) and (ii), we get
A( ΔADX ) = A( ΔACY )
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