Geometry Standard for Grades 68
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
threedimensional geometric shapes and develop mathematical arguments about
geometric relationships 
 precisely describe, classify, and understand relationships among types of
two and threedimensional 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 twodimensional representations of threedimensional 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.


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