Unit 1 Vocab
Vocab for Unit1
A translation slides a figure without turning it. Every point in the figure goes the same distance in the same direction. For example, Figure A was translated down and to the left, as shown by the arrows. Figure B is a translation of Figure A.
- We describe a translation with a vector that we write as (x+?, y+?)
A rotation turns a figure about a point, called the center of the rotation. Every point on the figure goes in a circle around the center and makes the same angels . The rotation can be clockwise, going in the same direction as the hands of a clock, or counterclockwise, going in the other direction. For example, Figure A was rotated clockwise around its bottom vertex. Figure C is a rotation of Figure A.
- To describe a rotation we need a direction (CW/CCW) an amount (Degrees), and a center of rotation C.O.R.
A reflection places points on the opposite side of a reflection line. The mirror image is a backwards copy of the original figure. The reflection line shows where the mirror should stand. For example, Figure A was reflected across the dotted line. Figure D is a reflection of Figure A.
- We Describe a reflection with the Line of Reflection
We use the word image to describe the new figure created by moving the original figure. If one point on the original figure moves to another point on the new figure, we call them corresponding points.
When a figure is on a grid, we can use the grid to describe a transformation. For example, here is a figure and an image of the figure after a move.
Quadrilateral ABCD is translated 4 units to the right and 3 units down to the position of quadrilateral A’B’C’D'.
A second type of grid is called an isometric grid. The isometric grid is made up of equilateral triangles. The angles in the triangles all measure 60 degrees, making the isometric grid convenient for showing rotations of 60 degrees.
A move, or combination of moves, is called a transformation. When we do one or more moves in a row, we often call that a sequence of transformations. To distinguish the original figure from its image, points in the image are sometimes labeled with the same letters as the original figure, but with the symbol attached, as in A' (pronounced “A prime”).
sequence of transformations
- A sequence of transformations is a set of translations, rotations, reflections, and dilations on a figure. The transformations are performed in a given order.
This diagram shows a sequence of transformations to move Figure A to Figure C. First, A is translated to the right to make B. Next, B is reflected across line to make C.
- The coordinate plane is a system for telling where points are. For example. point R is located at (3,2) on the coordinate plane, because it is three units to the right and two units up.
- A vertex is a point where two or more edges meet. When we have more than one vertex, we call them vertices.
Corresponding When part of an original figure matches up with part of a copy, we call them corresponding parts. These could be points, segments, angles, or distances.
- For example, point in the first triangle corresponds to point in the second triangle. Segment corresponds to segment .
Rigid Transformation A rigid transformation is a move that does not change any measurements of a figure. Translations, rotations, and reflections are rigid transformations, as is any sequence of these.
vertical angles Vertical angles are opposite angles that share the same vertex. They are formed by a pair of intersecting lines. Their angle measures are equal. For example, angles AED and CEB are vertical angles.
Congruent One figure is congruent to another if it can be moved with translations, rotations, and reflections to fit exactly over the other.