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).