Recently I ran into professor Halfbrain on the street. The professor told me that he had been spending his time with cutting triangles into smaller triangles. The professor has made the following amazing discovery:
Professor Halfbrain's theorem:
Every triangle can be cut into exactly $77$ smaller triangles that all are isosceles.
Is the professor's theorem indeed true, or has the professor once again made one of his phenomenal mathematical blunders?
(Recall that an isosceles triangle is a triangle, in which two or all three sides have equal length. This puzzle only considers so-called non-degenerate triangles, that is, triangles in which all three sides have strictly positive length.)