The Total solution for NCERT class 6-12
ABCD is a trapezium withAB || 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 thatΔADX and ΔACX lie on the same base AX and are between the same parallels AB andDC.
∴Area (ΔADX) = Area (ΔACX) … (1)
ΔACY and ΔACX lie on thesame base AC and are between the same parallels AC and XY.
∴Area (ΔACY) = Area (ACX) … (2)
From equations (1) and(2), we obtain