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.