Basic on Postulates
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Transcript of Basic on Postulates
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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.
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Geometry in Nature
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Symmetry in Nature
Symmetry Can Be Found All Around Us.
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Polygons
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Spheres in Nature
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1st Activity:Find anything in the classroom that will
indicate the following terms.
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• 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
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Basic Postulates
• Determination Postulates• Intersection Postulates• Separation Postulates
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Determination Postulates
• Line determination• Plane determination• Space determination
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Determination Postulate
Line determination: At least two points determine a line.
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Determination Postulate
Plane determination: At least three non collinear points determine a plane.
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Determination Postulate
Space determination: At least four non- coplanar points determine a space.
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Intersection Postulates
• Line intersection• Plane intersection• Space intersection• Line-space intersection
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Line Intersection:
Line a
Line bC
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Intersection Postulate
Line Intersection:If two different lines intersect, their intersection is a point.
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Plane IntersectionA
B
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Intersection Postulate
Plane Intersection: If two different planes intersect, their
intersection is a line.
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Space Intersection
Plane h
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Space Intersection
C
D
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Space Intersection
V
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Intersection Postulate
Space Intersection:If two different spaces intersect, then
their intersection is a point, a line or a plane.
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Plane-Line Intersectiont
T
R
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Plane-Line Intersection
B
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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.
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2nd Activity:
Answer the following questions and choose between a point, line, plane and
space.
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What is the intersection of?
Two rulers
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What is the intersection of?
A wall and a ceiling
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What is the intersection of?
Two classrooms
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What is the intersection of?
A flagpole on the ground
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What is the intersection of?
A paper and a ballpen
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Separation Postulates
• Line separation• Plane separation • Space separation
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Line Separation
R
S
T
T
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Line Separation:A point separates a line into two half- lines.
Separation Postulates
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Plane SeparationA
B
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Plane Separation
Plane p
A
B Plane o
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Separation Postulates
Plane Separation:A line separates a plane into half-
planes.
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Space Separation
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Space Separation
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Separation Postulates
Space Separation: A plane separates a space into two
half-spaces.
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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.
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Keeping in mind the following undefined terms in geometry, determining their
intersections and separations, how can we apply it in real world situation?
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As an ordinary Christian student, how can you explain yourself from being a point
in this world to make a big space for salvation?