Sliced Parallelogram: OEMO 2003 Advanced Q4: Upper Secondary Mathematics Competition Question

In a parallelogram ABCD, let E be the midpoint of the side AB and F the midpoint of BC. Let P be the intersection point of the lines EC and F D.

Show that the segments AP, BP, CP and DP divide the parallelogram into four triangles with areas in 1 : 2 : 3 : 4 ratio.


[OEMO 2003 Federal Advanced Q4]

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