From Gogeometry
Using :
- Define H’ rotation of H with angle –90° and center A
- =>AH=AH’ and BH’=DH=b
- => BH’ ⊥DH <=> BH’ ⊥BG
- ∠HAG=45° and ∠HAH’=90° => ∠GAH’=45°
- ΔGAH is congruent to ΔGAH’ (SAS)
- => GH’=GH=x
- BH’=b, BG=a, BH’ ⊥BG and GH’=x => ΔGBH’ is a rectangle triangle in B
- Therefore x^2=a^2+b^2