Points, Lines and Planes Objectives: (1)To identify and model points, lines, and planes (2)To identify collinear and coplanar points and intersecting lines and planes in space.

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) 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 “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 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 A B C W X Y Z d

Understanding Points and Lines A, B, and C are said to be: – Collinear Are A, B, and D collinear? – No A B C D

Planes 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 A B C D

Understanding Planes 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 A B C D E F

Interpret Sketches 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. T A B C D E F G