ABCD is a trapezium with . A line parallel to AC intersects AB at X and BC at Y. Prove that .
[Hint: Join CX.]
We have a trapezium ABCD, AB || CD
XY ||AC meets AB at X and BC at Y. Join XC
Since ADX and ACX lie on the same base CD and between same parallels AX and CD
Therefore, ar(ADX) = ar(ACX)..........(i)
Similarly ar(ACX) = ar(ACY).............(ii) [common base AC and AC || XY]
From eq (i) and eq (ii), we get