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## Geometry

 Instructional programs from prekindergarten through grade 12 should enable all students to-- analyze characteristics and properties of two- and three-dimensional 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 one-fourth 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.

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