Geometry Ch 9 - Transformations

Question 1

A transformation of a geometric figure is…

Answer 1

…a change in its position, shape, or size. When you assemble a jigsaw puzzle, you often move the puzzle pieces by flipping them, sliding them, or turning them. Each move is a type of transformation. The photos below illustrate some basic transformations that you will study.

Question 2

Preimage

Answer 2

The original figure in a geometric transformation.

Question 3

Image

Answer 3

The resulting figure of a geometric transformation.

Question 4

Isometry

Answer 4

A transformation in which the preimage and image are congruent.

Question 5

Translation (slide)

Answer 5

An isometry that maps all points of a figure the same distance in the same direction.

Question 6

Composition of transformations

Answer 6

a combination of two or more transformations. Each transformation is performed on the image of the preceding transformation. The composition of any two translations is also a translation.

Question 7

Reflection (flip)

Answer 7

An isometry in which a figure and its image have opposite orientations. thus a reflected image in a mirror appears “backwards.”

Question 8

Rotation

Answer 8

A transformation that turns a figure about a fixed point called the center of rotation. Rays drawn from the center of rotation to a point and its image form an angle called the angle of rotation.

Question 9

A figure has symmetry if…

Answer 9

… there is an isometry that maps the figure onto itself.

Question 10

Reflection / Line / Mirror / Mirror-Image Symmetry

Answer 10

Reflection symmetry, line symmetry, mirror symmetry, mirror-image symmetry, is symmetry with respect to reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. … An object or figure which is indistinguishable from its transformed image is called mirror symmetric.

Question 11

Rotational Symmetry

Answer 11

A figure that is its own image for some rotation of 180º or less.

Question 12

Point Symmetry

Answer 12

A figure that has 180º rotational symmetry.

Question 13

Dilation

Answer 13

A transformation whose preimage and image are similar. Thus, it is a similarity transformation. It is not, in general, an isometry. Every dilation has a center and a scale factor n, n > 0. the scale factor describes the size change from the original figure to the image. The dilation is an enlargement if the scale factor is greater than 1. The dilation is a reduction if the scale factor is between 0 and 1.

Question 14

A translation or rotation is…

Answer 14

… a composition of two reflections.

Question 15

A translation is…

Answer 15

… a composition of reflections across two parallel lines.

Question 16

A rotation is…

Answer 16

… a composition of reflections across two intersecting lines.

Question 17

Fundamental Theorem of Isometries

Answer 17

In a plane, one of two congruent figures can be mapped onto the other by a composition of at most three reflections.

Question 18

Glide Reflection

Answer 18

The composition of a glide (translation) and a reflection across a line parallel to the direction of translation.

Question 19

Isometry Classification Theorem

Answer 19

There are only four isometrics. They are the following:

Reflection
Translation
Rotation
Glide Reflection

Question 20

Tessellation (Tiling)

Answer 20

A repeating pattern of figures that completely covers a plane, without gaps or overlaps. You can create them with translations, rotations, and reflections.

Question 21

Objects that tessellate

Answer 21

Every triangle tessellates.

Every quadrilateral tessellates.

Question 22

Semiregular Tessellation is made from…

Answer 22

… two or more regular polygons.