Geometry Standard for Grades 912
Instructional programs from
prekindergarten through grade 12 should enable all students to— 
In grades 9–12 all students
should— 
Analyze characteristics and properties of
two and threedimensional geometric shapes and develop mathematical arguments
about geometric relationships 
 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.

Specify locations and describe spatial
relationships using coordinate geometry and other representational systems 
 use Cartesian coordinates and other coordinate systems, such as
navigational, polar, or spherical systems, to analyze geometric situations;
 investigate conjectures and solve problems involving two and
threedimensional objects represented with Cartesian
coordinates.

Apply transformations and use symmetry to
analyze mathematical situations 
 understand and represent translations, reflections, rotations, and dilations
of objects in the plane by using sketches, coordinates, vectors, function
notation, and matrices;
 use various representations to help understand the effects of simple
transformations and their compositions.

Use visualization, spatial reasoning, and
geometric modeling to solve problems 
 draw and construct representations of two and threedimensional geometric
objects using a variety of tools;
 visualize threedimensional objects and spaces from different perspectives
and analyze their cross sections;
 use vertexedge graphs to model and solve problems;
 use geometric models to gain insights into, and answer questions in, other
areas of mathematics;
 use geometric ideas to solve problems in, and gain insights into, other
disciplines and other areas of interest such as art and
architecture.


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