Basic Postulates in Geometry

Mrs. LeeDr. Koroleva

August 2006The Preuss School UCSD

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In your notes start a table as shown.

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Point-Line-Plane Postulatea. Unique Line AssumptionThrough any two points, there is exactly one line.

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Point-Line-Plane Postulateb. Number Line AssumptionEvery line is a set of points that can be put into a one-to-one correspondence with the real numbers, with any point on it corresponding to 0 and any other point corresponding to 1.

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Point-Line-Plane Postulatec. Dimension Assumption1) Given a line in a plane, there is at least one point in the plane that is not on the line.2) Given a plane in a space, there is at least one point in space that is not in the plane.

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Line Intersection TheoremTwo different lines intersect in at most one point.

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Definition of Parallel LinesTwo coplanar lines m and n are parallel lines, written m||n, if and only if they have no points in common or they are identical.

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Distance Postulatea. Uniqueness PropertyOn a line, there is a unique distance between two points.

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Distance Postulateb. Distance FormulaIf two points on a line have coordinates x and y, the distance between them is |x-y|.

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Distance Postulatec. Additive PropertyIf B is on , then AB+BC=AC.

AC