The author presents a proof that when given triangle $ABC$, point $P\ne S$ is a foot of a perpendicular from $C$ on $AB$, and $S$ is the middle of $AB$, then if angle $ACS$ equals angle $PCB$, then angle $BCA$ is a right one.

The article deals with some possibilities of how to teach mathematics through practical activities. The matematics in this conception is not a theoretical field. It is the area of the creation of mathematics by students themselves. Some examples are given.