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.

- Name three non-collinear points.

- Name the plane two different ways.

- Name a pair of opposite rays.

W

X

Z

Y

V

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

Where does Plane ABCD intersect

Plane ACEG?

What plane contains the points

C, D, and B?

What plane contains the points

E, F, and C?

Example

A

C

B

E

G

F

H

D

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