Good day

[![enter image description here](https://i.stack.imgur.com/KKMZP.jpg)](https://i.stack.imgur.com/KKMZP.jpg)

As part of a problem I need to show that AB is parallel to CD, with the given info on the image. All the segments marked red are equal, all 1-stripe grey equal etc.

I'd like to prove EA=AD, then it should prove AB||DC

Suggestions/tips? I'd appreciate pointers rather than a complete answer so as to try it self first!

Can we do the following?

[![enter image description here](https://i.stack.imgur.com/At8pK.jpg)](https://i.stack.imgur.com/At8pK.jpg)

We the right-angles on AC. Now we draw in AI parallel to EF. We then have parallelogram AIFH - thus $\angle AHF$ and $\angle AIF$ are both 90 degrees. Thus $\angle HAI$ = $\angle IFH$ = 90 degrees. Thus AB||DC ?