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Geometry Grade 8
|Understand congruence and similarity using physical models, pictorial representations, transparencies, or geometry software. [P] [L] [R]
1. Verify experimentally the properties of rotations, reflections, and translations:
a. Lines are taken to lines, and line segments to line segments of the same length.
b. Angles are taken to angles of the same measure. [P]
c. Parallel lines are taken to parallel lines.[P]
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. [L]
3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. [A]
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. [R]
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 thatthe sum of the three angles appears to form a line, and give an argumentin terms of transversals why this is so.