Vocabulary for "Transformations"
Congruent – exactly the same size and shape. Symbol:
Image – the resulting figure after an original figure is transformed in some way.
TYPES OF TRANFORMATIONS
Translation – when a shape, angle, line, etc. is moved horizontally and/or vertically. Also known as a slide. The image stays congruent to the original.
Example: Triangle ABC has been translated right and down (as seen in image DEF)
Rotation - when a shape, angle, line, etc. is turned around a point a certain number of degrees. The point can be in the figure or outside of it. The image stays congruent to the original. Example: Triangle ABC (from above) has been rotated about 90o clockwise to form image triangle A’B’C’.
Reflection - when a shape, angle, line, etc. is flipped across a line to form a mirrored image. The image stays congruent to the original. Example: Triangle ABC has been reflected across the line segment shown.
Dilation - when a shape, angle, line, etc. is enlarged or shrunk proportionally (looks the same, only larger or smaller) from a point. The image is usually not congruent to the original. Example: Triangle ABC has been enlarged by a scale factor of 2 to form Triangle MNP and has been shrunk by a scale factor of 0.25 to form triangle WXY
Translations - direction and number of "spaces" needed.
Reflections - line of reflection needed (the line you reflect across).
The axes are common reflection lines, but any line is possible. Here are some examples of other lines that you could reflect across.
Rotations - point of rotation (the point you rotate the figure around), number of degrees rotated, and direction of rotation are needed.
Here are some patterns we noticed when rotating around the origin (0,0)
Dilations - point of dilation and scale factor are needed.
NAMING vs. CLASSIFYING
Naming a figure, line, angle, etc. is to point out one particular figure, line, angle, etc.
Classifying tells the type of geometric figure.
Parallel – two or more lines, segments or rays that do not and would not (if extended) ever intersect. They never get closer together or farther apart. Symbol:
Perpendicular – lines, segments or rays that intersect at 90o angles. Symbol:
Transversal – a lines, segment or ray that intersects parallels.
Supplementary angles – two or more angles that add to 1800.
Complementary angles – two or more angles that add to 90o.
Vertical angles – congruent angles across from each other when two lines, segments or rays intersect.
Corresponding angles – congruent angles in the same location on different parallel lines intersected by a transversal. [Also used to describe angles in the same relative place in congruent and similar figures when in the same orientation].
*Alternate interior angles – congruent angles between parallels but on opposite sides of the transversal.
*Alternate exterior angles – congruent angles outside parallels but on opposite sides of the transversal.