hard problem i'm stuck on (cumulative problem- u can help!)

[Van Allen]

i need to finish this before i move on tomorrow. any help? thanks

Points M and N are the midpoints of opposite sides of paralellogram ABCD. Prove that:
a) R and S trisect diagonal BD
b) R is a points of trisection of AN and S is a point of trisection of MC.

 

[Gene]

Something like
BMC congruant to AND SAS
NDR congruant to MBS SAS
BS=RD
BMS similar to BAR AAA
BM=AM bisection
BM/(BM+AM) = BM/2BM = 1/2
BS/BR = 1/2
BS = SR
BS=SR=RD