The side length of the square EFGB is B, and the point C is on EB.

The side length of the square EHIA is c, and the point h is on FG.

Let IJ⊥AG cross j, HI cross AG cross k, AE cross CD cross l;

EA = EH = a，EB=EF=b，∠EBA=∠EFH=90，

∴ Rt△EFH≌Rt△EBA，∠ 1=∠2，FH=BA=a

∴ Rt△EFH，

Right angle FH=a, right angle EF=b, hypotenuse EH=c,

∠∠2 =∠3 =∠4 = 90-∠EAB，∠ 1=∠2，

∴ ∠ 1=∠3，EH=AI=a，∠ EFH =∠ AJI = 90，

∴ Rt△EFH≌Rt△AJI，JI=FH=a

∠∠5 =∠3 = 90-∠AIJ，∠3=∠4，

∴ ∠4=∠5, and DA=JI=a, ∠ ADL =∠ Ijk = 90,

∴ Rt△ADL≌Rt△IJK

∠∠6 =∠ 1 = 90-∠EHF，∠ 1=∠2，

∴ ∠2=∠6，EC=HB=b-a，∠ LCE =∠ KGH = 90。

∴rt△lce≌rt△kgh；

∴ To sum up: square ABCD area+square EFGB area

= square EHIA area;

Namely: a? +b？ =c？ ;

In a right triangle, the sum of the squares of two right-angled sides is equal to the square of the hypotenuse.