# The second famous theorem of Pythagoras

Everyone knows the **first famous theorem of Pythagoras** from school. The second, exceptional in importance, geometric theorem, attributed to Pythagoras, is the theorem on the sum of the angles of a triangle, equal to two right angles.

Historians of mathematics are trying to figure out how the brilliant mathematician proved this theorem.

Probably, he started with right-angled triangles and, by complementing rectangles (Fig. 1), tried to prove the correctness of the theorem in question.

Then he noticed that each triangle can be divided by the perpendicular dropped from the vertex into two right-angled triangles, and both of them can be completed to two rectangles (Fig. 1).

It is possible, however, that Pythagoras proved his theorem using a straight line drawn through the apex of the triangle parallel to the base (Fig. 2).

However, in this case, one must admit that he previously knew the theorem now attributed to Euclid about two parallel lines intersected by a third line.

In conclusion, it should be said that the second famous Pythagorean theorem turned out to be no less important in the development of mathematics than the first. Both of them are the foundation on which many outstanding theorems of modern mathematics were built.