# Proof of the Pythagorean theorem

President Garfield found proof of the Pythagorean theorem. Here’s how it goes!

Start with two rectangles triangle with legs a and b and hypotenuse view that it is the same triangle.

Put the two triangles on the other side so that the legs a and b form a straight line.

It is sufficient to rotate the triangle on the right by 90 degrees counterclockwise. Then move it to the left until it touches the triangle on the left.

Link endpoints to a Trapeze like the one see you below: label angles inside triangles, as shown below. This will help to prove that the triangle in the environment (one side is red) is a right triangle important thing to notice is that there are 3 triangles and developed, these triangles form a trapezoid

Therefore, zone 3 triangles must be equal to the area of trapezoid

The area of triangle ABC is (base × height) / 2

The area of triangle ABC = (a × b) / 2

The triangle to the right is the same triangle, the region is also (a × b) / 2

Now, what of the triangle in the medium or one with one side red?

Note that angle m + n angle = 90 degrees. And m + n + f = 180 degrees

90 + f = 180

f = 90 degrees

The triangle in the middle is a right triangle. Thus, the height is also equal to the base of c and

Area = (c × c) / 2 = c2 / 2

Trapezoid area = h/2 × (b1 + b2)

Trapezoid area = ((a_+_b)/2) × (a + b)

Finally, translate “the area of the 3 triangles must be equal the area of the trapezoid” in an equation

(a × b) / 2 + (a × b) / 2 + c2 / 2 = ((a_+_b) / 2) × (a + b)

(a × b + a × b) / 2 + c2 / 2 = ((a_+_b) / 2) × (a + b)

(2 × b) / 2 + c2 / 2 = (a + b) 2 / 2

All this that multiply by 2

2 a × b + c2 = (a + b) 2

2 a × b + c2 = a2 + 2 a × b + b2

Subtract 2 a × b on both sides:

C2 = a2 + b2

The proof of the Pythagorean theorem is complete!