President Garfield found proof of the Pythagorean theorem. Here’s how it goes!
Put the two triangles on the other side so that the legs a and b form a straight line.
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
Now, what of the triangle in the medium or one with one side red?
90 + f = 180
f = 90 degrees
Area = (c × c) / 2 = c2 / 2
Trapezoid area = h/2 × (b1 + b2)
Trapezoid area = ((a_+_b)/2) × (a + b)
(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!