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.]

Solution

ABCD is a trapezium with,AB || DC, XY || AC

Construction

Join CX

To Prove:

ar(ADX) = ar(ACY)

Proof:

ar(ΔADX) = ar(ΔAXC) ————(1) (They are on the same base AX and in-between the same parallels AB and CD)

ar(ΔAXC)=ar(ΔACY) ————(1)(They are on the same base AC and in-between the same parallels XY and AC)

From equation (1) and (2),

ar(ΔADX) = ar(ΔACY)

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