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Pythagorean Theorem Proof
Unit 4 ProjectGrace Olson
Four equal Right Triangles
a
aa
a
b
bb
b
cc
cc
Find the area of the Large Square
a
b
a
b c
a
b
c
a
bcc
Find the area of the large square:
The area of a square = a side squared
The side is = a + b
The are of the square = (a + b)
= (a + b)(a + b)
= a + 2ab + b
2
22
Find the area of a Triangle
a
b
a
b c
a
b
c
a
bcc
The area of the Triangles = ½ ab
Find the area of Four Triangles
a
b
a
b c
a
b
c
a
bcc
The area of the four triangles =
4(½ ab) = 2ab1 2
3 4
Find the area of the Small Square
a
b
a
b c
a
b
c
a
bcc
The area of the Small Square = c 2
Restate the area of the Large Square
a
b
a
b c
a
b
c
a
bcc
The area of the Large Square = the area of the Small Square + the area of the Four Triangles
The area of the Small Square = c
+
The area of the Four Triangles =
4(½ ab) = 2ab
c + 2ab
2
1 2
3 4
2
2
Set the areas equal
a
b
a
b c
a
b
c
a
bcc
c + 2ab = a + 2ab + b Simplify
c + 2ab = a + 2ab + b
c = a + b
1 2
3 4
22
22 2
2
2 22
