The first unit from the 8th-grade curriculum centers around geometry standards related to transformations – translations, reflections, rotations, and dilations, both on and off the coordinate plane – and the notion of congruence and similarity. Students will understand congruence and similarity using physical models, transparencies, or geometry software. Students learn to use informal arguments to establish proof of angle sum and exterior angle relationships related to parallel lines and two-dimensional polygons.
Transformations, Congruences, & Similarity
Understand congruence and similarity using physical models, transparencies, or geometry software.
MGSE8.G.1 Verify experimentally the congruence properties of rotations, reflections, and translations: lines are taken to lines and line segments to line segments of the same length; angles are taken to angles of the same measure; parallel lines are taken to parallel lines.
MGSE8.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.
MGSE8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two‐ dimensional figures using coordinates.
MGSE8.G.4 Understand that a two‐dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two‐dimensional figures, describe a sequence that exhibits the similarity between them.
MGSE8.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 three angles appear to form a line, and give an argument in terms of transversals why this is so.