Principles and Standards for School Mathematics

Geometry Standard

Geometry Standard (pre-K - 2)

recognize, name, build, draw, compare, and sort two- and three-dimensional shapes;


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describe attributes and parts of two- and three-dimensional shapes;


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investigate and predict the results of putting together and taking apart two- and three-dimensional shapes.


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Geometry Standard (3 - 5)

identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes;


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classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids;


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investigate, describe, and reason about the results of subdividing, combining, and transforming shapes;


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explore congruence and similarity;


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make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions.


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Geometry Standard (6 - 8)

precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties;


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understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects;


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create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.


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Geometry Standard (9 - 12)

analyze properties and determine attributes of two- and three-dimensional objects;


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explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them;


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establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others;


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use trigonometric relationships to determine lengths and angle measures.


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