1. Chapter 1: Essentials of Geometry
Section 1.1: Identify Points, Lines, and Planes

2. Section 1.1: Identify Points, Lines, and Planes
Goal: Use postulates and undefined terms
3 Undefined words in Geometry:
Point, Line, and Plane
Why are they undefined? These words cannot be mathematically defined using other mathematically known words

3. Section 1.1: Identify Points, Lines, and Planes
Point: has no dimension, is represented by a small dot Line: has one dimension, extends in two directions without end, represented by a line with two arrowheads Plane: has two dimensions, represented by a shape that looks like a floor or wall, extends without ending and has no thickness

4. Section 1.1: Identify Points, Lines, and Planes
Postulate 1: Two Points Determine a Line
Through any two points there is exactly one line
Postulate 2: Three Points Determine a Plane
Through any three points not on a line there is exactly one plane

5. Section 1.1: Identify Points, Lines, and Planes
Naming: A point has one letter name: Ex: point A A line can have a letter name or is named by 2 of its points Ex: line m or BC A plane can have a letter name or is named by 3 of its points Ex: plane P or plane DEF A C B m E F D P

6. Section 1.1: Identify Points, Lines, and Planes
Collinear points: points that lie on the same line
Coplanar points: points that lie on the same plane
Coplanar lines: lines that lie on the same plane

7. Section 1.1: Identify Points, Lines, and Planes
Space: the set of all points Line Segment: consists of two endpoints and all points between them Name by the two endpoints: GH Ray: consists of one endpoint and continues without end in one direction Name by the endpoint and one other point in the direction of the arrow: JK (note: the first letter is always the endpoint!) G H J K

8. Section 1.1: Identify Points, Lines, and Planes
Try together: Pg. 5 #1-7 (all) Homework: Pg. 5 #8-26 (all), 43, 44