Towards Understanding Triangle Construction Problems

Straightedge and compass construction problems are one of the oldest and most challenging problems in elementary mathematics. The central challenge, for a human or for a computer program, in solving construction problems is a huge search space. In this paper we analyze one family of triangle construction problems, aiming at detecting a small core of the underlying geometry knowledge. The analysis leads to a small set of needed definitions, lemmas and primitive construction steps, and consequently, to a simple algorithm for automated solving of problems from this family. The same approach can be applied to other families of construction problems.