Points Lines and Planes Objectives 1 To identify

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 noncollinear 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: A • B C – AB, BA, BC, CB, AC, CA W • • X • List all possible names for the line: – WX, XW, WY, YW, WZ, ZW, XY, YX, XZ, ZY, YZ, ZY • Name the line: –d d Y • • Z

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 • 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 D • • B • C

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 D • • B • E • F • C

Interpret Sketches D • 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. A • • E B • • F • G T C •