basic on postulates
TRANSCRIPT
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 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?