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)

Question

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]

Philoid · Accepted Answer

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) (i)

ΔACY and ΔACX lie on the same base AC and are between the same parallels AC and XY

Area (ΔACY) = Area (ACX) (ii)

From equations (i) and (ii), we obtain

Area (ΔADX) = Area (ΔACY)