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## Geometry Standard for Grades 6-8

 Expectations
 Instructional programs from prekindergarten through grade 12 should enable all students to— In grades 6–8 all students should— Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties; understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects; create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship. Specify locations and describe spatial relationships using coordinate geometry and other representational systems use coordinate geometry to represent and examine the properties of geometric shapes; use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides. Apply transformations and use symmetry to analyze mathematical situations describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling; examine the congruence, similarity, and line or rotational symmetry of objects using transformations. Use visualization, spatial reasoning, and geometric modeling to solve problems draw geometric objects with specified properties, such as side lengths or angle measures; use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume; use visual tools such as networks to represent and solve problems; use geometric models to represent and explain numerical and algebraic relationships; recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life.