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.