ok so from the updated link,
IFH, IGH, and GHF are right triangles
since IFH is a triangle, IF is a straight line (180 degrees)
angle IGH is 90 so therefor angle FGH is also a right angle aka IGH=FGH
GHI+GHF=90
all angles in a triangle =180
therefor, IGH+GHI+GIH=180
FGH+GHF+HFG=180
IGH+GHI+GIH=FGH+GHF+HFG
since IGH=FGH subtract that from both sides
GHI+GIH=GHF+HFG
also, since IGH=FGH=90, 180-90=90 so
GHI+GIH=GHF+HFG=90
we also know that
GHI+GHF=90
therefor
GIH=GHF and GHI=HFG
sorry if this is confusing extremelly confusing
so
we know that if 3 angles ina triangle are congruent, trignles are similar
so we know that
GHF=GIH and
HIF=GIH and
GHI=GFH
the answer is A
