Proof of Pythagorean theorem

What is Pythagorean theorem

The theorem states the sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c):

If this is depicted with squares:

image is from wikipedia "Pythagorean theorem"

Proof

The theorem can be proved algebraically using four copies of the same triangle arranged around a square with side c. This results in a larger square, with side a + b and area (a + b)². 

image is from wikipedia "Pythagorean theorem"

The four triangles and the square side c must have the same area as the larger square,

giving,

So

References

Wikipedia, "Pythagorean theorem", 2024 Apirl 28th visited