As shown in figure (1), A, E, F and C are on the same straight line, AE=CF, E and F are DE⊥AC and BF⊥AC respectively. If AB=CD, is G the midpoint of EF?

Because AE=CF

So AE+EF=CF+EF

So AF=CE

It should be BF vertical CE, so ∠BFA equals 90.

It should be DE vertical AC, so ∠DEC=90.

In ABF and CDE.

AB=CD

AF=CE

So RT△ABF=RT△CDE

So ∠BAE=∠DCF.

In △ABF and triangular CDF

∠BAE=∠DCF

AB=CD

∠BGA=∠CGD

So △ABF= triangle CDF

So af=cf

Because AE=CF

So EG=FG