A proof of the converse of the Pythagorean proposition

The article presents a demonstration of the converse of the Pythagorean Theorem based on the reductio ad absurdum. This is necessary to overcome the discrepancy, noticed by pupils, between the Euclidean purpose to demonstrate that the given triangle is right-angled and the auxiliary figure by which the given triangle is drawn as if it were already a right-angled one. To the eyes of students this does not make the Euclidean reasoning clear.