1 2 Points Lines and Planes Basic Geometry

1 -2: Points, Lines, and Planes Basic Geometry Terms

Undefined Terms Definition of words Consist of other words How do you define the first word? Philosophy Class? Every end has a start Every effect has a cause Geometry undefined terms Point, line, and plane Used to build the definitions of other figures

Undefined Terms Point – indicates a location and has no size Line – represented by a straight path that extends in two opposite directions without end and has no thickness. A line contains infinitely many points. Plane – represented by a flat surface that extends without end and has no thickness. A plane contains infinitely many lines.

Undefined Terms Collinear Points – points that lie on the same line Coplanar – when points and/or lines lie on the same plane

Defined Terms Segment – part of a line that consists of two endpoints and all points between them. Ray – part of a line that consists of one endpoint and all the points of the line on one side of the endpoint Opposite rays – two rays that share the same endpoint and form a line

Example Use the diagram to answer each question. - Name two coplanar lines. Y Z - Name three non-collinear points. V X - Name the plane two different ways. - Name a pair of opposite rays. W

Take Home Message Undefined terms are used as building blocks of Geometry (and Math) Geometry will have a lot of vocabulary words The concepts will give us algebraic equations Geometry will enhance our artistic abilities

1. 2 Continued Postulate – accepted statement of fact Like undefined terms, used as building blocks of the logical system in geometry Also known as axioms Postulate 1. 1 - through any two points, there is exactly one line Postulate 1. 2 - if two distinct lines intersect, then they intersect in exactly one point.

1. 2 Continued Postulate 1. 3 - if two distinct planes intersect, then they intersect in exactly one line

1. 2 Continued Postulate 1. 4 – through any three noncollinear points, there is exactly one plane

Example A Where does Plane ABCD intersect Plane ACEG? B D C What plane contains the points F E C, D, and B? G What plane contains the points E, F, and C? H

Take Home Message Postulates are assumed to be true No formal proof Relationship between dimensions A point is the intersection of two lines A line is the intersection of two planes A plane is the intersection of 3 D figures