Definition

Point: a location in space. A point has no size, but is represented by a dot labeled with a capital letter.

Q A P Z

Definition

Space: the set of all points

Definition

Line: a series of points that extends without end in two opposite directions. P Q l

Definition

Collinear: points that lie on the same line. R P Q

Practice

In the figure below, name three points that are collinear and three points that are not collinear.

Points

Y

,

Z

, and

W

lie on a line, so they are collinear.

For example,

X

,

Y

, and

Z

and

X

,

W

, and

Z

form triangles and are not collinear.

Definition

Plane: a flat surface that extends in all directions without end.

Practice

Shade the plane that contains

X

,

Y

, and

Z

.

Practice

Name the plane shown in two different ways.

You can name a plane using any three or more points on that plane that are not collinear. Some possible names for the plane shown are: plane

RST

plane

RSU

plane

RTU

plane

STU

plane

RSTU

Definition

Coplanar: points and lines that are in the same plane.

1.

Practice

How many planes are represented by the surfaces of the cube?

2.

Name the plane of the front of the cube in two different ways.

3.

a.

Name a point that is coplanar with the given points: E, F, G b.

B, C, G

Definition

Postulate: an accepted statement of fact.

Four Basic Postulates

1-1: Through any two points there is exactly one line.

1-2: If two lines intersect, then they intersect in exactly one point.

1-3: If two planes intersect, then they intersect in a line.

1-4: Through any three noncollinear points there is exactly one plane.

Homework

Points, Lines, and Planes in Student Practice Packet (Page 3, #1-21)