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

Undefined Terms Definition of words Philosophy Class? 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 Y Use the diagram to answer each question. Z Y V Use the diagram to answer each question. Name two coplanar lines. Name three non-collinear points. Name the plane two different ways. Name a pair of opposite rays.

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

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 3D figures