Question

Question 13
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).

Answer 1

It can be observed that $\Delta ADX$ and $\Delta ACX$ lie on the same base AX and are between the same parallels AB and DC.
$\Delta Area\left(\Delta ADX\right)=Area\left(\Delta ACX\right)...\left(1\right)$
$\Delta ACY$ and $\Delta ACX$ lie on the same base AC and are between the same parallels AC and XY.
$\therefore Area\left(\Delta ACY\right)=Area\left(ACX\right)...\left(2\right)$
From equations (1) and (2), we obtain, $Area\left(\Delta ADX\right)=Area\left(\Delta ACY\right)$