3 Tutor System
Starting just at 265/hour

# 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, $$\triangle{ADX}$$ and $$\triangle{ACX}$$ lie on the same base AX and are between the same parallels AB and DC.

$$\therefore$$ Area ($$\triangle{ADX}$$) = Area ($$\triangle{ACX}$$) ...(i)

Also, $$\triangle{ADY}$$ and $$\triangle{ACX}$$ lie on the same base AC and are between the same parallels AC and XY.

$$\therefore$$ Area ($$\triangle{ACY}$$) = Arca ($$\triangle{ACX}$$) ...(ii)

From Equations (i) and (ii), we get,

Area ($$\triangle{ADX}$$) = Area ($$\triangle{ACY}$$)

Hence, proved.