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

  7. Use the figure below. Name all segments that are parallel to AE. Name all segments that are skew to AE. Parallel segments lie in the same plane, and the lines that contain them do not intersect. The three segments in the figure above that are parallel to AE are BF, CG, and DH. Skew lines are lines that do not lie in the same plane. The four lines in the figure that do not lie in the same plane as AE are BC, CD, FG, and GH.

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

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

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

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

  12. 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

  13. Shade the plane that contains X, Y, and Z. Points X, Y, and Z are the vertices of one of the four triangular faces of the pyramid. To shade the plane, shade the interior of the triangle formed by X, Y, and Z.

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