Points, Lines, and Planes

Points, Lines, and Planes

GeometryMrs. King

Unit 1, Lesson 2

Definition

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

A

PQZ

Definition

Space: the set of all points

Definition

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

PQ

l

Definition

Collinear: points that lie on the same line.

PQ

R

For example, X, Y, and Z and X, W, and Z form triangles and are not collinear.

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.

Practice

Definition

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

Shade the plane that contains X, Y, and Z.

Practice

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 RSTplane RSUplane RTUplane STUplane RSTU

Name the plane shown in two different ways.

Practice

Definition

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

Practice1. 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. Name a point that is coplanar with the given points:a. 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)