Question

I need to prove that A’B’= A’D’ but i keep going in circles.

You have the figure in the picture, the hypothesis are:
AA’= (1/2)AB
BB’=(1/2)BC
CC’=(1/2)CD
DD’=(1/2)DA

These are all vectors!

Answer 1

It can't be proven because it isn't so.

You can show that A'B' = C'D' because each is half of AC (from the midsegment theorem).