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G.CO.A.1
G.CO.A.1

Geometry 9 - Piscataway High School
Geometry 9 - Piscataway High School

... Identify basic geometry vocabulary (points, lines, planes) Use undefined terms such as points, lines and planes to create axiomatic system to build other defined geometric terms (i.e. line segment, ray, coplanar, parallel, collinear, postulate, midpoint, segment bisector) Construct a copy of a line ...
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... Know and apply that if a line is perpendicular to each of two intersecting lines at their point of intersection, then the line is perpendicular to the plane determined by them (Define perpendicular lines and right angles) Know and apply that through a given point there passes one and only one plane ...
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Geometry - Piscataway High School

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Geometry - Piscataway High School

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Geometry - Piscataway High School

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... Two or more coplanar circles with the same center are called concentric circles. Two circles are congruent/ equal if they have congruent/equal radii. A point is in the interior of a circle if its distance from the center is less than the radius. A point is in the exterior of a circle if its distance ...
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Geometry 1st Semester Test * Ch

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Cartesian coordinate system



A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin, usually at ordered pair (0, 0). The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines). In general, n Cartesian coordinates (an element of real n-space) specify the point in an n-dimensional Euclidean space for any dimension n. These coordinates are equal, up to sign, to distances from the point to n mutually perpendicular hyperplanes.The invention of Cartesian coordinates in the 17th century by René Descartes (Latinized name: Cartesius) revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra. Using the Cartesian coordinate system, geometric shapes (such as curves) can be described by Cartesian equations: algebraic equations involving the coordinates of the points lying on the shape. For example, a circle of radius 2 in a plane may be described as the set of all points whose coordinates x and y satisfy the equation x2 + y2 = 4.Cartesian coordinates are the foundation of analytic geometry, and provide enlightening geometric interpretations for many other branches of mathematics, such as linear algebra, complex analysis, differential geometry, multivariate calculus, group theory and more. A familiar example is the concept of the graph of a function. Cartesian coordinates are also essential tools for most applied disciplines that deal with geometry, including astronomy, physics, engineering and many more. They are the most common coordinate system used in computer graphics, computer-aided geometric design and other geometry-related data processing.
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