Since we have that GD = BC, then, by the transitive property:
[tex]\begin{gathered} GD=BC=FH \\ \Rightarrow GD=FH \end{gathered}[/tex]Now, FH=AE, then, again by the transitive property:
[tex]\begin{gathered} GD=FH=AE \\ \Rightarrow GD=AE \end{gathered}[/tex]Therefore, AE=GD