Isometries

Definition of Transformation In a plane, a mapping is a transformation if each preimage point has exactly one image point, and each image point has exactly one preimage point.

Types of Transformations dilation – A figure can be enlarged or reduced. preimage image

rotation – A figure can be turned. preimage image

Translation - A figure can be slid. preimage image

reflection – A figure can be flipped. preimage image

When a geometric figure and its transformation image are congruent, the mapping is called an isometry or a congruence transformation.

Defn. of Isometry (Congruence Transformation) In a plane, an isometry is a transformation that maps every segment to a congruent segment.

The symbol is used to indicate a mapping The symbol is used to indicate a mapping. For example, means each point in is mapped onto exactly one point of When a figure and its transformation image are similar, the mapping is called a similarity transformation.

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