Unit B Flashcards
Preimage
The original image
Transformation
An operation that moves or changes a geometric figure in its position, shape, or size to produce a new figure.
Image
The new or resulting figure. It’s labeled with prime (‘)
Isometry
A transformation in which the preimage and image are congruent (reflections, translations, rotations, not dilations)
Reflection
Creates a mirror image of the original figure. (Flip)
Line of Reflection
A reflections that maps a figure onto itself. The reflection line is the line of symmetry.
Translation
Map or move every point in the same direction in the same distance. It is an isometry. (Slide)
Center of Rotation
Point in which a figure is rotated. (Counter - Clockwise)
Rotational Symmetry
When a figure is a rotation image of itself
-180 degrees or less
Point Symmetry
- exactly 180 degree rotational symmetry
Theorem 12 - 1
A translation or rotation is a combination of 2 reflections.
Theorem 12-2
A composition of 2 reflections in 2 parallel lines is a translation.
Theorem 12-3
A composition in 2 intersecting lines is a rotation.
Fundemental Theorem of Isometries
In a plane, 1 of 2 congruent figures can be mapped onto each other by a composition of at most 3 reflections.
Glide Reflection
Composition of a translation and a reflection in a line parallel to the glide vector.
2-D Symmetry
Reflectional
Rotational
Point
3-D Symmetry
Plane
Axis
Plane Symmetry
When a plane can be sliced through a 3-D figure, creating 2 congruent 3-D figures on either side.
Axis Symmetry
When an axis can be placed in the 3-D figure, and the figure is its own image for some rotations of 180 degrees or less.
