How Does One Cut a Triangle? I

Abstract

You are familiar with a picture of three midlines drawn in an arbitrary triangle T (see Figure 2.1).

The midlines cut T into four triangles congruent to each other. You probably know that this construction can be easily generalized to all perfect squares.

All we have to do is partition each side of T into n segments of equal length (see Figure 2.2) and connect the corresponding marks of partitions by lines parallel to the sides of the triangle T (you should prove that we indeed get n ² congruent triangles).