What are isometries?

The ISOMETRY (ISO - equal, METRY - measure) is a geometric transformation that changes a figure in another one that is geometrical equal, that is, it neither changes the length of the segments of the figure nor the amplitude of its angles. Thus, the only thing that changes in an isometry is the position of the figure. There are four types of isometries: the translations; the rotations; the reflections (regarding an axis or a point) and the sliding reflection.

Could you better explain the translation?

The translation is an isometry that consists in the displacement of a figure according to a direction, sense and length. All the points of the original figure are displaced according to the same way and all the segments of a line that belong to the original figure are transformed into parallel segments of a line having the same length.

Could you better explain the rotation?

A figure corresponds to symmetry of rotation (or rotational) if it coincides with itself more than once during the whole turn. Concerning the regular polygons, the amount of rotation symmetries equals the amount of the sides of the polygon.

Could you better explain the reflection?

We say a figure corresponds has a reflection, symmetry (or axial reflection) when it accepts at least one axis of symmetry. Concerning regular polygons, the amount of reflection symmetry equal the amount of the sides of the polygon.

Could you better explain the sliding reflection?

A sliding reflection consists of a geometric transformation involving a certain axis and then it is followed by a translation throughout that same axis. Or as an alternative, it can first occur the translation and then the reflection of an axis which is parallel to the direction of the translation.

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