A

Basic Geometric Terms

Vocabulary found in Chapter 1 Section 2: Point , Space , Line , Collinear , Plane , Coplanar B t Lines can often be named in more ways than one.

Ex: AB (line AB) or line t

1. How many ways can you name the following line?

R S T 2. Is there any difference between RS, ST and TR? Explain

Planes too can be named in more ways than one. Ex:

P B A C

plane P plane ABC

3. Why must a Plane be named with 3 non-collinear?

Every point on TS lies on both planes.

3A. Therefore any set of collinear points lie on infinite different planes not just one.

R S T W E H D F G A, B, F, E are coplanar A, B, F, H are not coplanar C

4. Can three points be non-coplanar?

A B

Basic Postulates

A Postulate is an accepted statement of fact.

Postulate :

Through any two points there is exactly one line. Line t is the only line that passes through points A and B.

A Postulate :

If two lines intersect, then they intersect at exactly one point.

Think about a system of equations in algebra. One, none , or infinite solutions .

Postulate :

If two planes intersect, then they intersect in a line. Plane RST and plane STW intersect in ST.

Postulate :

Through any three noncollinear points there is exactly one plane.

Think of a Triangle. You can’t draw two different triangles with the exact same three points.

R

B

S T W

t

1. 3 RS, RT, ST (because ST and TS are the same line using the same points we do not count them twice) 2. No, they continue on forever in the same two directions containing all the same points.

4. No, If three points are collinear then we know they are coplanar, and if three points are non-collinear then they can be connected to form a triangle thus creating a plane. Therefore any three points are always coplanar.