Transformation Geometry in High School

The purpose of this paper is to discuss the introduction of transformations into the tenth-grade geometry course. A transformation is defined to be: a correspondence (or rule, mapping, function) which carries each point P of the plane (or a space) into some unique point P\u27 of that plane or space. [ (8)1, page 273 ]. Transformation geometry is the study of invariance under a group of ... transformations. [ (8)1 ,page 274 ]. Thus, the basis of a tenth-grade course in transformation geometry is different from that of the traditional course: Transformations instead of congruent triangles. This is explained in the introduction to Chapter I. The theory of congruent triangles has its proper place later in the course. (Chapter II, Section G). The other sections in Chapter I deal with several considerations which seem to be necessary before the work on the transformations can begin:.