If ABCDEF a regular hexagon,and FCGH is a square and AB=4 , FC=8 prove that the triangle IED is similar to the triangle IGH .
This reminds me a joke. A visitor to Odessa, a "capital of Soviet humor," asks a local resident: "If I go down this street, will there be a railway station?" The local replies, "The station will be there even if you don't go." In this case, triangles IED and IGH are similar even if AB is not 4.
It is easy to show that the two triangles have their corresponding angles equal since ED is parallel to HG.
I used the word "corresponding" in its general meaning to mean "matching." E.g., angle IED corresponds to angle IGH and not angle HIG. I agree that IED and IGH are alternate interior angles, not corresponding in the technical sense of angles produced by a transversal.