Question

People have discovered dozens of different ways to prove the Pythagorean theorem. Here is another interesting example: Consider this diagram of a square inscribed in another square. Each shaded area is a right triangle. We can calculate the area of the white square by finding the area of the big square and subtracting the area of the four small blue triangles:

Answer 1

please help heres a visual

Answer 2

What aspects of the diagram do you understand?

Answer 3

Do you know pythagorean's theorem?

Answer 4

Yes I know Pythagorean theorem. a2 + b2 = c2 is it the first equation minus the other ?

Answer 5

@ybarrap

Answer 6

$$
\Large \rm area ~ of ~ white ~ square = (a+b)^2- 4\frac{1}{2}ab
\\ \Large =(a+b)(a+b) - 2ab
\\ \Large = a^2 + ab + ab + b^2 - 2ab
\\ \Large = a^2 + 2ab + b^2 - 2ab
\\ \Large = a^2 + b^2

$$

Answer 7

And then using the fact that the area of the white square is also
$$
c^2
$$

You see now that
$$
a^2+b=c^2
$$

Thus, proving Pythagorean's Theorem