Note that by symmetry, the 4 statements are equivalent.
I think the easiest way to go is to show that the normal vectors of both planes are parallel.
1. Define AB and AC.
2. Cross-product to get the normal vector.
3. Define EF and EG.
4. Cross-product to get the normal vector .
5. Cross-product both normal vectors and get 0 (meaning they are parallel and hence that the planes are parallel).