Triangle ABC similar triangles EBF similar triangles AED, angle C equals angle FED and angle EFC equals angle EDC, which proves that EDCF is a parallelogram. It is concluded that ed equals FC, because BD bisects angle ABC, so angle ABD equals angle CBD, because ED is parallel to BC, so angle EDB equals angle DBC, so angle e BD equals angle EDB, so ED equals EB, so EB equals FC.