The Basics and Important

Postulates of Geometry

POSTULATE No. 1

You can only draw one line between two points. You will not be able to draw a second line through points A and B.

EXAMPLE:

POSTULATE No. 2:A line has infinite points.

POSTULATE No. 3:

One plane contains infinite points.

EXAMPLE:

POSTULATE No. 4:Two lines can instersect at ONLY one point. S is the only intersection of and

in the figure below.

EXAMPLE:

POSTULATE No. 5:When two planes intersect, their

intersection is a line.

EXAMPLE:

POSTULATE NO. 6:Infinite lines pass by a point.

Example:

Infinite planes pass by a line.

POSTULATE No. 7:

Example:

POSTULATE No. 8: Three planes intersect in a point.

POSTULATE No. 9: Three points that are not colineal form a plane.

• THREE POINTS THAT ARE NOT COLINEAR ARE ALWAYS COPLANEAR.

• IF THREE POINTS ARE NOT COLINEAR THEN THERE ONLY EXIST ONE PLANE THAT CONTAINS THEM.

EXAMPLE : 3 POINTS THAT ARE NOT COLINEAR FORM A PLANE.

MORE EXAMPLES:

POSTULATE 10:Two lines that intersect form a plane.

• Two lines that intersect are always coplanear.

• If two lines intersect there only exist one plane containing them.

EXAMPLE:

POSTULATE 11: A line and a point outside form a

plane.How?

1. We choose one new point on the line.

2. We draw a line across both points.

3. TWO LINES THAT INTERSECT FORM A PLANE.

PLEASE IDENTIFY SITUATIONS IN WHICH YOU RECOGNIZE THE

GEOMETRY POSTULATES AND ON A CARDBOARD, DO A COLLAGE WITH

MAGAZINE PICTURES OF THESE SITUATIONS, BY CHOOSING EXAMPLES OF AT LEAST 5

POSTULATES.