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;
 specify locations and describe spatial relationships using coordinate
geometry and other representational systems;
 apply transformations and use symmetry to analyze mathematical
situations;
 use visualization, spatial reasoning, and geometric modeling to solve
problems.

Geometry and spatial sense are fundamental
components of mathematics learning. They offer ways to interpret and reflect on
our physical environment and can serve as tools for the study of other topics in
mathematics and science.
Geometry is a natural area of mathematics for the
development of students' reasoning and justification skills that build across
the grades. As the study of the relationships among shapes and their properties
becomes more abstract, students should come to understand the role of
definitions and theorems and be able to construct their own proofs. For example,
students in high school should be able to prove that the area of a triangle
formed by vertices that bisect the sides of a larger triangle equals onefourth
of the area of the larger triangle.
Principles and
Standards calls for geometry to be learned using concrete models, drawings,
and dynamic software. With appropriate activities and tools and with teacher
support, students can make and explore conjectures about geometry and reason
carefully about geometric ideas.