Transformation geometry

For example, within transformation geometry, the properties of an isosceles triangle are deduced from the fact that it is mapped to itself by a reflection about a certain line.

[1] The first systematic effort to use transformations as the foundation of geometry was made by Felix Klein in the 19th century, under the name Erlangen programme.

Andrei Kolmogorov included this approach (together with set theory) as part of a proposal for geometry teaching reform in Russia.

An exploration of transformation geometry often begins with a study of reflection symmetry as found in daily life.

Educators have shown some interest and described projects and experiences with transformation geometry for children from kindergarten to high school.

In the case of very young age children, in order to avoid introducing new terminology and to make links with students' everyday experience with concrete objects, it was sometimes recommended to use words they are familiar with, like "flips" for line reflections, "slides" for translations, and "turns" for rotations, although these are not precise mathematical language.