Math

Current Math Unit: 8.1 Rigid Transformations and Congruence

Standards Addressing: GEOMETRY

  1. 8.G Understand congruence and similarity using physical models, transparencies, or geometry software. 
  2. 8.G.1 Verify experimentally the properties of rotations, reflections, and translations (include examples both with and without coordinates). a. Lines are taken to lines, and line segments are taken to line segments of the same length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines.
  3. 8.G.2 Understand that a two-dimensional figure is congruent  to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. (Include examples both with and without coordinates.)
  4. 8.G.3 Describe the effect of dilationsG, translations, rotations, and reflections on two-dimensional figures using coordinates.
  5. 8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

In this unit, students learn to: 

  • understand and use the terms “reflection,” “rotation,” “translation,”
  • recognize what determines each type of transformation, e.g., two points determine a translation.
  • understand and use the terms “transformation” and “rigid transformation.”
  • identify and describe translations, rotations, and reflections, and sequences of these, using the terms “corresponding sides” and “corresponding angles,” and recognizing that lengths and angle measures are preserved.
  • draw images of figures under rigid transformations on and off square grids and the coordinate plane.
  • use rigid transformations to generate shapes and to reason about measurements of figures.
  • understand congruence of plane figures in terms of rigid transformations.
  • recognize when one plane figure is congruent or not congruent to another.
  • use the definition of “congruent” and properties of congruent figures to justify claims of congruence or non-congruence.