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Sec. 1 – 2 Points, Lines, & Planes

Sec. 1 – 2 Points, Lines, & Planes. Objectives: 1) Understand the basic terms of geometry. 2) Understand the basic postulates of geometry. 3 Undefined Terms of Geometry. Point Is a location. Represented by a small dot & by a capital letter. Reads: Point A. A.

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Sec. 1 – 2 Points, Lines, & Planes

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  1. Sec. 1 – 2 Points, Lines, & Planes Objectives: 1) Understand the basic terms of geometry. 2) Understand the basic postulates of geometry.

  2. 3 Undefined Terms of Geometry • Point • Is a location. • Represented by a small dot & by a capital letter. • Reads: Point A A

  3. 3 Undefined Terms Continues Line Is a series of points that extend in two opposite directions w/o end. Defined by any two points on that line. Name a line by 2 capital letters or 1 lower case letter. Points that lie on the same line are called Collinear Points. Notation is important: AB or line t AC BC CA BA t C A B

  4. The last of the Undefined Terms • Plane • A flat surface that extends indefinitely • Contains lines and points • Named by 3 Noncollinear points or by a capital script letter. • Points & lines in the same plane are coplanar. • Notation: PQR or Plane R Q P R R

  5. Space – Is defined as the set of all points

  6. Defined Terms • A segment is part of a line that consists of two endpoints and all points between them. • Segments are named by their endpoints. • A ray is part of a line that consists of one endpoint and continues in the other direction. • Rays are named by their endpoint and another point on the ray (the order of the points indicates the direction of the ray!).

  7. Defined Terms, con’t • Opposite rays are two rays that share the same endpoint and form a line. • How would you name the opposite rays above?

  8. Ex.1: Name some planes and lines. A B D C H E G F

  9. A postulate, or axiom, is a statement that is accepted as true without proof. Postulates about points, lines, and planes help describe geometric properties.

  10. Postulate – Is an accepted statement of fact. • Aka: Axiom • P(1 – 1) Through any two points there is exactly one line.

  11. P(1 – 2) If two lines intersect, then they intersect in exactly one point. k A r

  12. P(1 – 3) If two planes intersect, then they intersect in exactly one line.

  13. P(1 – 4) Through any three noncollinear points there is exactly one plane. A B Which plane contains the points: A, B, C Which plane contains the points: F, B, E Which plane contains the points: H, A, B D C H E G F

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