Chapter 11 (Sp12)

Chapter 11 (Sp12) - Section 11-1 Basic Geometry Notions...

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Section 11-1 – Basic Geometry Notions Geometry: “geo” means earth and “metron” means measure The fundamental building blocks of geometry are points, lines, and planes. Linear Notions: A line has no thickness, extends forever in two directions and is determined by 2 points. Points on the same line are called collinear . A line segment is a subset of a line that contains 2 endpoints. A ray is a subset of a line that contains one endpoint and continues forever in one direction. Planar Notions: A plane has no thickness and extends indefinitely in two directions and is determined by 3 points. Points and/or lines in the same plane are called coplanar . Skew lines are lines that do not intersect and no plane contains them. Intersecting lines are two coplanar lines with exactly one point in common. Concurrent lines are lines that contain the same point (not necessarily all in the same plane). 1
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Properties of Points, Lines, and Planes: 1. There is exactly one line that contains any two distinct points. 2. If two points lie in a plane then the line containing the points lies in the plane. 3. If two distinct planes intersect, then their intersection is a line. 4. There is exactly one plane that contains any three distinct noncollinear points. 5. A line and a point not on the line determine a plane. 6. Two parallel lines determine a plane. 7. Two intersecting lines determine a plane. A line and a plane can be related in one of 3 ways: 1. If they have no points in common, then the line and plane are parallel. 2. If two points of the line are in the plane, then the entire line is in the plane. 3. If only one point of the line is in the plane, then the line intersects the plane (cuts through). Example : Sketch the following a) Line AB is contained in Plane XYZ b) Line AB and Plane XYZ have only one point in common. c) Lines AB and CD are skew lines 2
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Example : Given 10 points (no 3 of which are collinear) how many lines can be drawn through the 10 points? Angles When two rays share an endpoint an angle is formed. The angle contains sides and a vertex.
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This note was uploaded on 01/06/2012 for the course MATH 1351 taught by Professor Lisajuliano during the Spring '12 term at Collins.

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Chapter 11 (Sp12) - Section 11-1 Basic Geometry Notions...

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