In a parallelogram ABCD, let F be the midpoint of the side AB and E the midpoint of BC. Let M be the intersection point of the lines ED and FC.
Show that the segments AM, BM, CM and DM divide the parallelogram into four triangles with areas in 1 : 2 : 3 : 4 ratio.
from
OEMO 2003 Advanced Q4: Upper Secondary Mathematics Competition Question
