Thales’s theorem

Another character who will cause a lot of trouble for our little schoolchildren.

Greek philosopher and mathematician who passed on to us the theorem in his name and who returns every year to the books and notebooks of college students and teachers.

I want to talk here about Thales.

As for the Pythagore’s theorem, Thales does us the honor of transmitting to us certain properties discovered with two secant lines crossed by two parallel lines as in the drawings below.

Thales’ theorem allows us to know if the two lines UV and WX are parallel.

Moreover, if there is not equality in the stated proportions, we can then say that the lines are not parallel.

We therefore use the Thales converse to demonstrate that the lines UV and WX are or are not parallel.

A small example for understanding and using Thales’ theorem.