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Points , Lines and Planes. Objectives : To identify and model points, lines , and planes To identify collinear and coplanar points and intersecting lines and planes in space. Definitions.

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Points lines and planes

Points, Lines and Planes

Objectives:

To identify and model points, lines, and planes

To identify collinear and coplanar points and intersecting lines and planes in space.


Definitions
Definitions

  • Point: a basic undefined term of geometry. A point is a location. In a figure, points are represented by a dot. Points are named by capital letters.

  • Line: A basic undefined term of geometry. A line is made up of points and has no thickness or width. In a figure, a line is shown with an arrowhead at each end. Lines are usually named by lowercase script letters or by writing capital letters for two points on a line, with a double arrow over the pair of letters.

  • Plane: A basic undefined term of geometry. A plane is a flat surface made up of points that has no depth and extends indefinitely in all directions. In a figure, a plane is often represented by a shaded, slanted 4-sided figure. Planes are usually named by a capital script letter or by three non-collinear points on the plane.


Definitions continued
Definitions (continued)

  • Collinear: Points that are on the same line.

  • Coplanar: Points that are on the same plane

  • Undefined term: Words, usually readily understood, that are not formally explained by means of more basic words and concepts. The basic undefined terms in geometry are point, line, and plane

  • Space: A boundless 3-dimensional set of all points.


Point
Point

  • “A location”

  • Represented by a dot

  • Named with a capital letter!

  • Can be referred as:

    A or point A

  • Has no thickness

A


Line

  • A string of points extending infinitely in two directions

  • Has arrowheads on both ends.

  • Named with a lower case letter…

    • Named b or line b

  • …Or with any TWO points on the line with a double headed arrow above it.

    • Named AB or BA

  • b

    A

    B


    Name the lines
    Name the Lines

    • Give 6 Possible names for the line:

      • AB, BA, BC, CB, AC, CA

    • List all possible names for the line:

      • WX, XW, WY, YW, WZ, ZW, XY, YX, XZ, ZY, YZ, ZY

    • Name the line:

      • d

    C

    B

    A

    W

    Y

    X

    Z

    d


    Understanding points and lines
    Understanding Points and Lines

    B

    C

    A

    • A, B, and C are said to be:

      • Collinear

    • Are A, B, and D collinear?

      • No

    • D


    Planes
    Planes

    A

    D

    • A “flat surface”

    • Represented by a parallelogram

    • Name by a capital letter; or 3 non-collinear points.

    • Plane A or Plane BCD

    • Has no thickness

    C

    B


    Understanding planes
    Understanding Planes

    A

    D

    • Name the plane with 1 letter:

      • Plane A

    • Name the plane by its points:

      • Plane BCE

    • Are B, C, E collinear?

      • No

    • Are B,C,D, and E coplanar?

      • Yes

    • Are B, C, D, and F coplanar?

      • No

    C

    B

    • E

    • F


    Interpret sketches
    Interpret Sketches

    D

    A

    How many planes appear in this figure?

    - 4; Plane FDG, Plane FED, Plane FEG, Plane T

    Name 3 collinear points:

    - A, B, C

    Are points B, E, G, and D coplanar? Explain:

    - No, D is not on plane T whereas B, E and G are on plane T.

    Where does AC intersect Plane T?

    - At B.

    E

    B

    G

    F

    T

    C


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