Geometry Chapter 8
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22 terms
Terms | Definitions |
|---|---|
 Transformation | A one- to- one correspondence between two sets of points |
| Translation | A transformation that takes a pre- image and slides the all the points an equal distance away (in the same direction, in a straight line) |
| Magnitude of the translation | The (equal) distance for all the lines connecting a pre- image to its translated image |
| Reflection | A transformation that takes a pre- image and reflects it across a line (mirror) of reflection, so that the distance from any point to the line is the same on both sides; the lines connecting the points of the pre- image/ image are perpendicular to the mirror of reflection |
| Magnitude of the reflection | The distance for all the lines connecting a pre- image to its reflected image; are not the same length |
| Rotation | A tranformation that takes a pre- image and rotates it around a fixed point- the center of rotation-, so that each angle is moved the same number of degrees; lines connecting the points to the center of rotation remain the same length |
| Magnitude of the rotation | The angle measure between the lines connecting the points of the pre- image/ image and the center of rotation; remain the same degrees |
| Dilation | A transformation where the side lengths are changed to make the image bigger/ smaller |
| Magnitude of the dilation (P) | Represented as a ratio- A'P'/AP; example is 2:2 (makes shape twice as large) |
| Isometry | A transformation retaining angle measurements/ side lengths; includes translations, reflections, and rotations, but not dilations |
| P; perpendicular bisector | The reflection of a point (P) through a line (l) is __ if P lies on the line; if not, it is point P', and l is the ________ _______of PP' |
| To reflect a point through a line (Construction) | Put the compass on the point and trace an arch through the line, so that the arch and line intersect two times; keep the compass the same and trace two more arcs from those newly- made points so the arcs touch; the point where these two arcs cross is the reflected point |
| Translation; twice | The result (composite) of two successive reflections across parallel lines is a ________; the distance from one point in the pre- image to the same point in the translated image is ____ the distance from the first line of reflection to the other |
| Rotation | The composite of two successive reflections across intersecting lines is a _______; the measure of the angle from a point in the pre- image to the same point in the rotated image is ____ the measure of the angle between the two lines of reflection |
| Congruent | Two figures are congruent if there is an isometry that makes one figure the image of the other |
| Glide reflection | The composite of a translation and a reflection in a line parallel to the direction of the translation; the composite of 3 reflections |
| Mirror image | An image made by an odd number of reflections |
| Rotation symmetry | With respect to a point, a figure iff it coincides with its rotation image through less than 360° around the point |
| N- fold rotation symmetry (replace 'n' with number of times it has symmetry) | A figure iff the smallest angle through which it can be turned to look the same is 360°/n |
| Reflection (line) symmetry | A figure with respect to a line (axis) iff it coincides with its reflected image through the line |
| Translation symmetry | A pattern iff it coincides with a translation image |
| Distances; angles; equal | Corresponding _____ and _____ in symmetric figures are ____ |
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