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a vertical look at key concepts and procedures geometry
a vertical look at key concepts and procedures geometry

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... Analyze attributes of 2-D and 3-D shapes and describe relationships between 2- and 3-D shapes. Identify, sketch, and build pyramids, cones, cylinders, and right prisms and relate them to the two-dimensional shapes (nets) of the objects. Identify and draw a 2-D representation of a three dimensional o ...
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... Use definitions, properties, and theorems to justify a statement. Write two-column proofs to prove theorems about lines and angles. Complete two-column proofs to prove theorems about segments. Complete two-column proofs to prove theorems about angles. Make conjectures about the angles formed by a pa ...
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Geometry A - Arkansas Department of Education

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Analytic geometry



In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.Analytic geometry is widely used in physics and engineering, and is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry.Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and squares, often in two and sometimes in three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space (three dimensions). As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometrical shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. The numerical output, however, might also be a vector or a shape. That the algebra of the real numbers can be employed to yield results about the linear continuum of geometry relies on the Cantor–Dedekind axiom.
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