Vocabulary: Transformation – a one-to-one correspondence between two sets of points Pre-image – the original figure Image – figure after transformation
Center of dilation – the point which is used as a reference point for a dilation Line of reflection – the mirror; the line over which an image is reflected Isometry – a transformation that preserves distance and angle measure
A reflection through line l of point P creates P’. Line l is then the perpendicular bisector of segment PP’.
Translation – the composite of two successive reflections through parallel lines Rotation – the composite of two successive reflections through intersecting lines › Center of rotation – the point about which a rotation occurs › Magnitude – the measure of the angle through which a point of the original figure turns to coincide with its rotation image
Vocabulary: Congruent – two figures are such if there exists an isometry such that one figure is the image of the other Glide Reflection – the composite of a translation and a reflection over a line parallel to the direction of the translation (in a sense, three or some greater odd number of reflections) Mirror Image – created by an odd number of reflections, two figures are the reverse of one another
They’re congruent.
Vocabulary: Rotation symmetry – a figure possesses this characteristic, with respect to a point, iff it coincides exactly with its rotation image when rotated less than 360˚ about the specific point (the center of the figure is usually said point) › A figure has point symmetry if it looks exactly the same turned upside down n-fold rotation symmetry – a figure has this iff the smallest angle through which it can be turned to look exactly the same is 360˚/n › A figure with point symmetry has 2-fold symmetry
Reflection (line) symmetry – a figure has this, with respect to a line, iff it coincides with its reflection image through the line › The line is sometimes called the axis Translation symmetry – a patter has such iff it coincides with a translation image