What is the Pythagorean theorem?

This theorem is one of the fundamental theorems in Euclidean geometry. The Pythagorean theorem establishes the regularity of the aspect ratio in a right-angled triangle.

This theorem has three formulations:

in a right-angled triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of its hypotenuse;
the area of ​​the square of a right-angled triangle built on the hypotenuse is equal to the sum of the areas of the squares built on its legs;
reverse formulation: a triangle whose sum of squares of the lengths of two sides is equal to the square of the length of the third side is rectangular.

Mathematical notation of the Pythagorean theorem
Suppose we have a triangle ABC in which the angle <A = 90. Therefore, based on this, we can assert that this triangle is right-angled.

In triangle ABC, the sides belonging to the angle <A = 90 (AB and AC) are its legs, and the side opposite the right angle <A is its hypotenuse, respectively (BC).

Therefore, based on the first formulation of this theorem and the assumptions stated above, we can write the following:

BC ^ 2 = AB ^ 2 + AC ^ 2