Establishes that the congruence criteria for polygons with more than three sides (such as ASASA for Quadrilaterals) are easily proved within the scope of the standard high school geometry course. Also argues that elegant applications of these criteria are more easily found once these new criteria are known. (PK)

Presents an attempt to combine the history of mathematics of ancient Greece with the course on theoretical geometry taught in Greek secondary schools. Three sections present the history of ancient Greek geometry, geometrical constructions using straightedges and compasses, and an application of Ptolemy's theorem in solving ancient astronomy…