Given : ABCD is a parallelogram. X and Y are midpoints of AB and CD respectively .
to prove : AYCX is a parallelogram and ar (AXCY): ar (ABCD)
proof : AB = CD & AB // CD
1/2 AB =1/2 CD & 1/2AB //1/2 CD
AX = CY &AX// CY
Therefore AYCX is a parallelogram.
ar of AYCX = 1/2 ar ABCD
Therefore the ratio is 1:2