The Greek philosopher thales of Miletus studied geometric properties and discovered two important theorems that are name after him.
We want to divide a segment into a number of equal parts and Thales' Theorem is very useful in this case. Next year we will use this Theorem to draw polygons and other constructions.
Using a compass and a ruler, we can divide a segment into a number of equal parts, the Thales' Theorem says:
"If two coplanar lines are intersected by a set of parallel lines, the segments created on one of the lines are proportional to those created on the other."
Coplanar means two lines that are in the same plane, for example, two lines in the blackboard are in the same plane wich is the blackboard.
Proportional means the relationship between this lines are always the same. For example, if two lines are equal between them in the auxiliary line they are going to be equal between them in the segment.
Let's see a video to help you:
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