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Mathematical Skills for Transformational Geometry

Transformational geometry is a method of changing the position of geometric figures on a plane. The original figure (pre-image) is copied, then called the image of the transformation. The study of transformational geometry aids in the mathematical concept of shape congruence. Congruent figures have the same size, area, angles and lengths of lines. It also reinforces thinking skills, teaches mathematical conventions and terminology and allows the student to transfer her knowledge and skills to other applications. There are three types of rigid transformation and one non-rigid transformation.
  1. Rotation

    • Rotation of a geometric shape is performed by rotating (turning) the shape around a fixed, central point. It is a rigid transformation where any specific point of the figure remains equidistant from the central point during the rotation. Rotations are measured in the number of degrees of a 360º circle, and are conventionally performed in a counterclockwise direction.

    Reflection

    • A reflection of a geometric shape is similar to seeing a mirror image of the original figure, and is a rigid transformation. The line dividing the two images is called the mirror line, and it can run in any direction. The transformational image is the same size as the pre-image, and each matching point in the two images is equidistant from the mirror line.

    Translation

    • Translation, another rigid transformation, is a geometrical term that means moving. When a translation is performed on a geometric figure, the figure changes position without rotation or resizing. Every point in the figure moves an equal distance to the new position. A translation is also called a slide.

    Resizing

    • Resizing is a non-rigid transformation. A transformation by resizing retains the original proportions among the elements of the figure, and all angles remain the same. The figure is simply made larger or smaller. Other names for resizing include dilation, compression, contraction, enlargement and expansion.

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