u/Guilty-Efficiency385

ABCD is a paralellogram. Prove that if the areas of the red regions are equal, then the areas of the green regions are equal as well.

So far I've got a bunch of loose identities and ratios but cant piece them to get a proof. Some necessary conditions: AE and FC must be the same length, so triangles HFC and AGE would have the same height. This also would require GH to be parallel to AC. These things are necessary but I havnt been able to show any of them to be true