Basic on Postulates

Basic about Postulates

Determine the different postulates that includes the characteristics of a point, line, plane and

space. Make a justification about the intersections and

separations of lines, planes and spaces. Apply the following concepts in real life situations.

Geometry in Nature

Symmetry

Symmetry in Nature

Symmetry Can Be Found All Around Us.

Polygons

Spheres in Nature

1st Activity:Find anything in the classroom that will

indicate the following terms.

• Postulate – is a statement that is accepted as true even

without proof.– Example: God exists

• Theorem– is a statement that is accepted as true only

after it has been proven.– Example: Sun is the center of the solar

system

Basic Postulates

• Determination Postulates• Intersection Postulates• Separation Postulates

Determination Postulates

• Line determination• Plane determination• Space determination

Determination Postulate

Line determination: At least two points determine a line.

Determination Postulate

Plane determination: At least three non collinear points determine a plane.

Determination Postulate

Space determination: At least four non- coplanar points determine a space.

Intersection Postulates

• Line intersection• Plane intersection• Space intersection• Line-space intersection

Line Intersection:

Line a

Line bC

Intersection Postulate

Line Intersection:If two different lines intersect, their intersection is a point.

Plane IntersectionA

B

Intersection Postulate

Plane Intersection: If two different planes intersect, their

intersection is a line.

Space Intersection

Plane h

Space Intersection

C

D

Space Intersection

V

Intersection Postulate

Space Intersection:If two different spaces intersect, then

their intersection is a point, a line or a plane.

Plane-Line Intersectiont

T

R

Plane-Line Intersection

B

Intersection Postulate

Plane-Line Intersection:If a plane and a line intersect, then

their intersection is either a point or a line. It is a point, if the line is not contained on the plane, and a line, if the line is contained on the plane.

2nd Activity:

Answer the following questions and choose between a point, line, plane and

space.

What is the intersection of?

Two rulers

What is the intersection of?

A wall and a ceiling

What is the intersection of?

Two classrooms

What is the intersection of?

A flagpole on the ground

What is the intersection of?

A paper and a ballpen

Separation Postulates

• Line separation• Plane separation • Space separation

Line Separation

R

S

T

T

Line Separation:A point separates a line into two half- lines.

Separation Postulates

Plane SeparationA

B

Plane Separation

Plane p

A

B Plane o

Separation Postulates

Plane Separation:A line separates a plane into half-

planes.

Space Separation

Space Separation

Separation Postulates

Space Separation: A plane separates a space into two

half-spaces.

3rd Activity:Determine if the following statements are true, otherwise it is false.

1. We can divide the tip of a pen into two.2. The division of a rectangular picture

frame edge is a point.3. We can cut a paper into two by a

line.4. When exactly two divides a cake, then

a plane separates them.

Keeping in mind the following undefined terms in geometry, determining their

intersections and separations, how can we apply it in real world situation?

As an ordinary Christian student, how can you explain yourself from being a point

in this world to make a big space for salvation?