Geometry Standard
Instructional programs from prekindergarten through grade
12
should enable all students to—

Analyze
characteristics and properties of two and threedimensional geometric
shapes and develop mathematical arguments about geometric relationships

PreK–2
Expectations:
In
prekindergarten through grade 2 all students should– 
• 
recognize, name, build, draw, compare, and sort two and
threedimensional shapes; 
• 
describe attributes and parts of two and threedimensional
shapes; 
• 
investigate and predict the results of putting together and
taking apart two and threedimensional shapes. 



Grades 3–5 Expectations:
In grades 3–5 all students should– 
• 
identify, compare, and analyze attributes of two and
threedimensional shapes and develop vocabulary to describe the
attributes; 
• 
classify two and threedimensional shapes according to their
properties and develop definitions of classes of shapes such as
triangles and pyramids; 
• 
investigate, describe, and reason about the results of
subdividing, combining, and transforming shapes; 
• 
make and test conjectures about geometric properties and
relationships and develop logical arguments to justify
conclusions. 



Grades 6–8 Expectations:
In grades 6–8 all students should– 
• 
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. 



Grades 9–12 Expectations:
In grades 9–12 all students should– 
• 
analyze properties and determine attributes of two and
threedimensional objects; 
• 
explore relationships (including congruence and similarity)
among classes of two and threedimensional geometric objects,
make and test conjectures about them, and solve problems
involving them; 
• 
establish the validity of geometric conjectures using deduction,
prove theorems, and critique arguments made by others;

• 
use
trigonometric relationships to determine lengths and angle
measures. 


