How to prove the Pythagorean theorem

A very popular subject in algebra is solving problems in a right triangle using the Pythagorean theorem . The theorem is a simple formula that shows the relationship between the sides of any right triangle. Basic knowledge of square and square root is required. If you want to learn how to prove the Pythagorean theorem, do not forget to read this article from.

one

A right triangle is simply a triangle that contains a right angle (90º). The longest side is called hypotenuse, and is often referred to as the "c". The other sides are called legs and are assigned the "a" and "b".

two

Assuming you have called your triangle in the same way, the following theorem applies. That is, the square on side "a" plus the square on side "b" is equal to the square on hypotenuse "c".

a² + b² = c²

Typically, in a problem with right triangles, they will give you the value of two of their sides, and you must always find the value of the missing side. It can be any of the three, so we have to remember to substitute in the formula correctly.

3

Suppose we have a triangle with the legs of length 3 and 4 and we have to find the hypotenuse. In this case, our missing side is the "c". Now look at the formula above. The first step is the substitution, in this case, the values ​​that we know of "a" and "b". The next step is to calculate the squares.

We still do not know the value of "c". We just know that c² = 25 and we should remember that the square root of x² is x.

4

As we pointed out in the previous step, in mathematics, if you take the square root of a square, you return to the original number. This is because the square and the square root are inverse operations. They undo each other, they are "crossed out".

5

With this said, since we want the value of "c" and not of c², the root of "c" goes with the square and, when calculating the root of 25, we obtain that the value of "c" corresponds to 5.

6

And if you want to verify that you have done it correctly, you will only have to substitute the values ​​of the legs and the hypotenuse in the initial formula of the Pythagorean Theorem and perform the calculation of the squares:

a² + b² = c²

3² + 4² = 5²

9 + 16 = 25

25 = 25

Indeed, we have solved the problem well and this is demonstrated by the Pythagorean Theorem.