Question

ABCD is a trapezium with AB $\parallel$ DC. A line parallel to AC intersects AB at X and BC at Y.
Prove that ar ($△$ADX) = ar ($△$ACY). [3 MARKS]

Answer 1

Statement of the theorem : 1 Mark
Application of the theorem : 1 Mark
Calculation : 1 Mark

Join CX.

It can be observed that $△$ADX and $△$ACX lie on the same base AX and are between the same parallels AB and DC.

$\therefore$ Area ($△$ADX) = Area ($△$ACX) ... (1)

$△$ACY and $△$ACX lie on the same base AC and are between the same parallels AC and XY.

$\therefore$ Area ($△$ACY) = Area ($△$ACX) ... (2)

From equations (1) and (2), we obtain

Area ($△$ADX) = Area ($△$ACY)