CHAPTER 1:

Tools of Geometry

Section 1-3:Points, Lines, and Planes

Objectives

To understand basic terms of geometry. To understand basic postulates of geometry.

Vocabulary

Point Space Line Collinear Points Plane Coplanar Postulate Axiom

Point

A point is a location. A point has no size. Represented by a small dot and capital letter. Geometric figures consist of sets of points.

Space

Space is defined as the set of all points.

Line

A line is a series of points that extends in two opposite directions without end.

Ways to name a line: Use any two points on the line. A single lowercase italics letter.

Collinear Points

Points that lie on the same line are collinear points.

Identifying Collinear Points

In the diagram, are E, F, and C collinear?

Are E, F, and D collinear?

Plane

A plane is a flat surface that has no thickness. A plane contains many lines and extends

without end in the direction of all of its lines. Naming a plane:

You may use a single capital letter. You may use three or more of its non-collinear

points.

Postulate (or Axiom)

A postulate (or axiom) is an accepted statement of fact.

Postulate 1-1:

Through any two points, there is exactly one line.

Postulate 1-2:

If 2 lines intersect, they intersect in exactly one point.

Postulate 1-3:

If two planes intersect, they intersect in exactly one line.

Finding the intersection of two planes.

Where do planes ABC and plane DZY intersect?

A

B

D

C

W

YX

Z

Postulate 1-4:

Through any three noncollinear points, there is exactly one plane.