∵ ∠BAF + ∠FAD = ∠DAE + ∠FAD = 90o,∴ ∠BAF=∠DAE.连结FB,在ΔABF和ΔADE中,∵ AB =AD = c,AE = AF = b,∠BAF=∠DAE,∴ ΔABF ≌ ΔADE.∴ ∠AFB = ∠AED = 90o,BF = DE = a.∴ 点B、F、G、H在一条直线上.在RtΔABF和RtΔBCG中,∵ AB = BC = c,BF = CG = a,∴ RtΔABF ≌ RtΔBCG . ∵c²=S₂+S₃+S₄+S₅ b²=S₁+S₂+S₆ a²=S₃+S₇S₁=S₅=S₄=S₆+S₇, ∴a²+b²=S₃+S₇+S₁+S₂+S₆=S₂+S₃+S₁+(S₆+S₇)=S₂+S₃+S₄+S₅ =c²∴ a²+b²=c².