angle ACH = 180 - 60 - 60 =60 degrees
BC=AC
CE=CD
angle BCE = angle ACD = 120 degrees
triangle BCE and ACD are congruent (S.A.S)
AC=BC
angle ACH = angle BCG = 60 degrees
angle HAC = angle GBC (corr . angles, congruent triangles)
so, triangle ACH and BCG are congruent (A.S.A)
so, CG=CH (corr. sides, congruent triangles)