Unit 6: Congruence and Similarity
The students will explore similarity and congruence. More specifically, they will be able to identify congruent and similar figures in the coordinate plane and use mapping rules to manipulate figures to insure congruence and/or similarity. Students will be able to identify angles and the relationships among angles associated with paralletl lines cut by transversals.
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.
8.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.
MP 7.Look for and make use of structure.
MP 3.Construct viable arguments and critique the reasoning of others.
8.G.1 Verify experimentally the properties of rotations, reflections, and translations:
8.G.3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
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.