Guys I need help and the internet is failing me.

I need to prove Wittenbauer's Parallelogram. This is what it looks like: Wittenbauer's Parallelogram from Interactive Mathematics Miscellany and Puzzles

Basically, any convex quadrilateral ABCD, if you trisect it's sides at S,T; U,V; W,X; Y,Z then TU, VW, XY, ZS form a parallelogram.

All I really have to work with is area and similarity and I'm just completely stumped. I've been staring at it for a while and just am not seeing what initial connection I have to make in order to see the proof.

Once I prove it's a parallelogram I have other stuff to prove and am hoping they follow easily afterward. Here is the other stuff:

Prove that |TU| = 2/3 |AC| and |VX| = 2/3 |BD|

and

If ABCD is a rhombus, prove that the figure formed by TU, VW, XY, ZS is a rectangle and that it's area is equal to 8/9 |ABCD|.