ABCD is a parallelogram, G is the point on AB such that AG = 2GB, E is a point of DC , such that CE = 2DE and F is th point of BC such that BF = 2FC. prove that :

1) ar (quad ADEG) = ar(quad GBCE)

2.) ar( triangle EBG) = 1/6 ar( quad ABCD)

3) ar( triangle EFC) = 1/2 AR(triangle EBF)

4 ) ar( triangle EBG )= ar( triangle EFC)

5 ) find what portion of the area of parallelogram is the area of triangle EFG.