Chapter 9: Geometry Vocab.

center of rotation

A center of rotation is a transformation with these two properties: *The image of Q is itself (that is, Q'=Q). *For any other point V, QV' = QV and m<VQV'=x.

composition of transformations

A composition of transformations is a combination of two or more transformations. In a composition, you perform each transformation on the image of the preceding transformation.

dilation

A dilation is a transformation with the following properties. *The image of C is itself (that is, C' = C). *For any other point R, R' is on CR and CR' = n X CR, or n = CR'/CR. *Dilations preserve angle measure.

enlargement

A dilation is an enlargement if the scale factor n is greater than 1.

rotational symmetry

A figure has a rotational symmetry, if its image, after a rotation of less than 360, is exactly the same as the original figure.

line symmetry

A figure has line symmetry, if there is a reflection for which the figure is its own image.

reflectional symmetry

A figure has line symmetry, if there is a reflection for which the figure is its own image.

point symmetry

A figure has point symmetry if a 180 rotation about a center of rotation maps the figure onto itself.

center of dilation

A fixed point in the plane about which all points are expanded or contracted.

glide reflection

A glide reflection is the composition of a translation (a glide) and a reflection across a line parallel to the direction of translation. You can map a left paw print onto a right paw print with a glide reflection.

line of reflection

A line of reflection is a transformation with the following properties: *If a point A is on line m, then the image of A is itself (that is, A'=A). *If a point B is not on line m, then m is the perpendicular bisector of BB'. You write the reflection across m that takes P to P' as R(m)(P)=P'.

reflection

A reflection is a transformation such that if a point A is on line r, then the image of A is itself, and if a point B is not on line r, then its image B' is the point such that r is the perpendicular bisector of BB'.

rotation

A rotation (turn) of x about a point R, called the center of rotation, is a transformation such that for any point V, its image is the point V', where RV=RV' and m<VRV'=x. The image of R is itself. The positive number of degrees x that a figure rotates is the angle of rotation.

transformation

A transformation of a geometric figure is a function, or mapping that results in a change in the position, shape, or size of the figure. When you play dominoes, you often move the dominoes by flipping them, sliding them, or turning them. Each move is a type of transformation.

rigid motion

A transformation that preserves distance and angle measures is called a rigid motion.

translation

A translation is a transformation that maps all points of a figure the same distance in the same direction.

congruence transformations

Because compositions of rigid motions take figures to congruent figures, they are also called congruence transformations.

similarity transformations

Compositions of rigid motions and dilations map preimages to similar images. For this reason, they are called similarity transformations. Similarity transformations give you another way to think about similarity.

preimage

In a transformation, the original figure is the preimage.

isometry

It means same distance. An isometry is a transformation that preserves distance, or length. So, translations, reflections, and rotations are isometries.

reduction

The dilation is a reduction if the scale factor n is between 0 and 1.

line of symmetry

The line of reflection is called the line of symmetry.

angle of rotation

The number of degrees a figure rotates is the angle of rotation.

image

The resulting figure is the image.

scale factor

The scale factor n of a dilation is the ratio of a length of the image to the corresponding length in the preimage, with the image length always in the numerator.

congruent

Two figures are congruent if and only if there is a sequence of one or more rigid motions that maps one figure onto the other.

similar

Two figures are similar if and only if there is a similarity transformation that maps one figure onto the other.

symmetry

You can use what you know about reflections and rotations to identify types of symmetry. A figure has symmetry if there is a rigid motion that maps the figure onto itself.