Because AH is perpendicular to BD and EF is perpendicular to BD,

So angle EFD= angle DHA=90 degrees,

So angle DEF+ angle EDF=90 degrees,

Because AD is perpendicular to DE,

So angle ADB+ angle EDF=90 degrees,

So angle DEF= angle ADB,

Because angle DEF= angle ADB, angle EFD= angle DHA, AD=DE,

So triangle DEF is equal to triangle ADH(A, a, s),

So EF=DH,

Similarly, triangle BCG is equal to triangle ABH,

So CG=HB,

So CG+EF=HB+DH=DB.