Points, Lines, and Planes Section 1-2 Points, Lines, and Planes

Introduction This first chapter will give you the necessary definitions to understand geometry Please remember the conventions given as that will be how you are expected to present a final answer Do what you can to remember these definitions That was a hint

Definitions Point Naming convention Partner Up A location Has no size and takes up no space Shown as a dot or a corner Usually labeled with a letter Naming convention Read as “point A” Written as ∙A Partner Up Give some real life examples of points

Definitions Line m Straight connector between two points Has no thickness Extends infinitely in both directions Labeled with at least two points or an italicized, lowercase letter at one end E F m

Definitions Naming conventions (previous examples) If given points Read as “line EF” or “line FE” Written as or If given the letter at the end Written as it’s read; “line m”

Definitions Plane Naming Conventions Partner Up A surface Has no thickness Usually shown as a shaded shape The most difficult of the three definitions Naming Conventions If given a group of points NOT on the same line Read and written as “plane DEF” If given a capital letter off by itself Read and written as “plane P” Partner Up Come up with 4 examples of planes

Other Definitions Collinear points Coplanar Two or more points on the same line Coplanar Two or more points or lines on the same plane

Example What are other ways to name line QT? V W m n What are other ways to name line QT? What are other ways to name plane P? Name a set of three collinear points. Name a set of four coplanar points.

More Definitions Line Segment Naming Conventions A measurable piece of a line Named by it two endpoints, but sometimes by a single capital letter Naming Conventions Read “segment AB” Written as or A B

More Definitions Ray Naming Conventions Half a line One end is fixed, the other goes forever Named like a line and a segment, but order is important Naming Conventions Read “ray DE” Written D E

More Definitions Opposite Rays Two rays that form a line with their shared endpoint Shown as a line with a third point in the middle Name the rays, not the line

Example 2 Identify the segments in the figure (6 answers) Identify the rays in the figure (6 answers) Identify the pair of opposite rays (1 answer)

Theories These are called postulates in the book These postulates are forensics to interpreting geometry Postulate 1-1 Through any 2 points, there is one line Postulate 1-2 Two lines intersect at one point Postulate 1-3 Two planes intersect at one line Postulate 1-4 Through any 3 noncollinear points there is one plane