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Exploring Geometry Basics: Points, Lines, and Planes

Learn about points, lines, and planes in geometry, understand collinear points, and explore the postulates that govern them. Practice identifying lines and planes in various examples.

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Exploring Geometry Basics: Points, Lines, and Planes

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  1. Chapter 1 1.2 Points, Lines, and Planes

  2. Point • A location, represented by a capital letter, has no size.

  3. Space • A set of points.

  4. A B • Named using: • AB or line m m Line • A series of points that extends in two opposite directions without end.

  5. D A C B m Collinear points • Points that lie on the same line • Points A, B, and C are collinear • Points A, C and D are noncollinear

  6. Plane • It is a flat surface that has no thickness. It contains many lines and extends without end in the directions of all of its lines. It is names either by a single capital letter, or by at least 3 noncollinear points.

  7. Coplanar • Points and lines that lie in the same plane are called this

  8. Postulate or axiom • An accepted statement of fact.

  9. POSTULATES: • 1-1: Through any two points there is exactly one line • 1-2: If two lines intesect, then they intersect in exactly one point. • 1-3: If two planes intersect, then they intersect in exactly one line. • 1-4: Through any three noncollinear points, there is exactly one plane.

  10. Example 1: . • Are the three points collinear? If so, name the line on which they lie. A, D, E ? B, C, D ? A, E, C ? Name line m in three other ways. m A . . G n B C D F E l

  11. Example 2 • Name the plane represented by each surface of the box. • The bottom • The top • The front • The back • The right side • The left side M A H D N R I T

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