This is my own original made proof for Pythagorean Theorem..I made my own figures to prove that Pythagorean Theorem has really a formula c2 = a2 + b2

1. Pythagorean Theorem
Grouped
Ungrouped
b
b
b b
b
b
bb
a
a a
a
a
a
a
a
c
c
c
c
c
c
c
c
b
b
a
c
c
a
c
c
b b
a a
a
b
cc
c
c
cc
c
c
c
cc
c
b b
baa
a

2. The area of the rectangle is equal to the sum of the areas of the small eight
triangles and two squares in the middle.
Based on the figure above,
From Geometry:
Area of the Rectangle = (length) x (width)
Base = 2a + 2b the base of the rectangle
Height = a + b the height of the rectangle
where: width = base
length = height
From the diagram;
= +
1
8( )
2
ab the area of the 8 small triangles
2
2( )c the area of the 2 squares in the
middle
Area of
the 8
small
triangles
Area of the
Rectangle
Area of
the 2
squares
(width) x (length) = Area of the 8 triangles + Area of the 2 squares
21
(2 2 )( ) 8( ) 2( )
2
a b a b ab c   
2 2 2
2 2 2 2 4 2a ab ab b ab c    
2 2 2
2 4 2 4 2a ab b ab c   
2 2
2 4 2 4 2a ab b ab c   
2 2 2
2 2 2a b c 
2 2 2
2( ) 2a b c 
2 2 2
2( ) 2
2 2
a b c

2 2 2
a b c  The formula for Pythagorean Theorem