AE⊥BF, angle BAM+ angle ABM = 90, angle CBF+ angle ABM = 90, then angle BAE= angle BAM= angle CBF,

And AB=BC, angle ABE= angle BCF, so △ Abe △ BCF, AE=BF.

2) Equality

Let a be AH parallel to GE and BF be n, and then prove it by 1.

(Note: The parallel lines between parallel lines are equal in length)

3) Synthesis 1) and 2)

I'd better figure it out myself.