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February 24, 2010
February 24, 2010

A Congruence Problem for Polyhedra
A Congruence Problem for Polyhedra

HSCC_Post and Thm PE.indd
HSCC_Post and Thm PE.indd

A SURVEY OF NIELSEN PERIODIC POINT THEORY (FIXED n)
A SURVEY OF NIELSEN PERIODIC POINT THEORY (FIXED n)

Parallel Lines and Transversals Investigation
Parallel Lines and Transversals Investigation

Geometry
Geometry

Mathematical Methods (CO-145)
Mathematical Methods (CO-145)

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2014c Geometry Khan Academy Video Correlations By SpringBoard

... • Use  slope  to  determine  whether  lines  are   Writing  Equations  of  Parallel  and  Perpendicular  Lines   parallel  or  perpendicular.   8-­‐2  Learning  Targets:   Equations  of  parallel  and  perpendicular  lines   • Write  the  equat ...
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SB Geometry Khan Correlations (1)

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Example - AllSaintsMath7-8

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9 CHAPTER Linear Relations

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Problem Solving Drill - Rapid Learning Center

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Linear Independence and Linear Dependence

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Farey Sequences, Ford Circles and Pick`s Theorem

Master of Arts in Teaching (MAT) - DigitalCommons@University of
Master of Arts in Teaching (MAT) - DigitalCommons@University of

Angle Pairs and One-Step Equations
Angle Pairs and One-Step Equations

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Check students` drawings. ∠GNL or ∠LNG ∠P

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Standards by Progression

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2 Reasoning and Proofs

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PPT

... Each person will have a unique number For each question, I will first give the class time to work out an answer. Then, I will call three different people at random They must explain the answer to the TAs and Gupta. If the TAs and Gupta are satisfied, your group gets points. The winning group will ge ...
Angles - chris west`s electronic portfolio
Angles - chris west`s electronic portfolio

Angles
Angles

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PPT

... Each person will have a unique number For each question, I will first give the class time to work out an answer. Then, I will call three different people at random They must explain the answer to the TAs (who are all the way in the back). If the TAs are satisfied, the class gets points. If the class ...
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Diagonals of Quadrilaterals_solutions.jnt

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4.3 - 4.5 Triangle Congruence Postulates

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Line (geometry)



The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth. Lines are an idealization of such objects. Until the seventeenth century, lines were defined in this manner: ""The [straight or curved] line is the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which […] will leave from its imaginary moving some vestige in length, exempt of any width. […] The straight line is that which is equally extended between its points""Euclid described a line as ""breadthless length"" which ""lies equally with respect to the points on itself""; he introduced several postulates as basic unprovable properties from which he constructed the geometry, which is now called Euclidean geometry to avoid confusion with other geometries which have been introduced since the end of nineteenth century (such as non-Euclidean, projective and affine geometry).In modern mathematics, given the multitude of geometries, the concept of a line is closely tied to the way the geometry is described. For instance, in analytic geometry, a line in the plane is often defined as the set of points whose coordinates satisfy a given linear equation, but in a more abstract setting, such as incidence geometry, a line may be an independent object, distinct from the set of points which lie on it.When a geometry is described by a set of axioms, the notion of a line is usually left undefined (a so-called primitive object). The properties of lines are then determined by the axioms which refer to them. One advantage to this approach is the flexibility it gives to users of the geometry. Thus in differential geometry a line may be interpreted as a geodesic (shortest path between points), while in some projective geometries a line is a 2-dimensional vector space (all linear combinations of two independent vectors). This flexibility also extends beyond mathematics and, for example, permits physicists to think of the path of a light ray as being a line.A line segment is a part of a line that is bounded by two distinct end points and contains every point on the line between its end points. Depending on how the line segment is defined, either of the two end points may or may not be part of the line segment. Two or more line segments may have some of the same relationships as lines, such as being parallel, intersecting, or skew, but unlike lines they may be none of these, if they are coplanar and either do not intersect or are collinear.
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