in ∆ABC,DAE is a straight line parallel to BC such thay DA=AE.if CD meets AB at X and BE meets AC at Y prove that XY is parallel to BC.

Since, triangle DAC and EAC are in the same base (since , DA = EA ) and b/w same parallels DE and BC => ar( DAC )= ar ( DAC ) =>ar(DAC - AXY ) = ar ( EAC - AXY ) =>ar(XBY) = ar(YCX ) Since, triangles XBY and YCX are on the same base and having same area => XY is parallel to BC ( converse of mid point theorem)