Is the side length of square ABCD a? Point b is on AG,
Is the side length of square EFGB b? , point c is on EB,
Is the side length of square EHIA c? , h point is on FG,
Let IJ⊥AG pass through j, HI pass through AG pass through k, AE pass through CD pass through l? ;
∵? EA=EH=a，EB=EF=b，∠EBA=∠EFH=90，
∴? Rt△EFH≌Rt△EBA，∠ 1=∠2，？ FH=BA=a？ ,
∴? At 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 &；; sup2+b & amp； sup2= c & ampsup2？ ;
∴? In a right triangle, the sum of the squares of two right-angled sides is equal to the square of the hypotenuse.