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).
[Hint: Join CX.]
It can be observed that ΔADX and ΔACX lie on the same base AX and are between the same parallels AB and DC.
∴ Area (ΔADX) = Area (ΔACX) ... (1)
ΔACY and ΔACX lie on the same base AC and are between the same parallels AC and XY.
∴ Area (ΔACY) = Area (ACX) ... (2)
From equations (1) and (2), we obtain
Area (ΔADX) = Area (ΔACY)