In the solution and proof of geometrical tasks routine use is made of theorems and their converse theorems. The problem is that a part, though very small, of the converse theorems is false and therefore the use of such theorems will produce mathematical mistakes and wrong results. Due to this risk, the students must be educated to verify before use that the converse theorem is indeed true.

We present six cases in which the converse theorem is not true. For each case, we present the additional requirements which when added to the theorem cause it to become true.

the converse theorem, sufficient conditions, use of computer technology (D.G.S.).