The document outlines the basic postulates of geometry, including definitions and justifications for points, lines, planes, and spaces, as well as their intersections and separations. It includes activities that encourage the application of these concepts to real-life situations, emphasizing the presence of geometry in nature. Additionally, it addresses undefined terms in geometry and prompts reflection on personal identity in relation to these concepts.

1. 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.

2. Geometry in Nature

3. Symmetry

4. Symmetry in Nature
Symmetry Can Be
Found All Around Us.

8. Polygons

14. Spheres in Nature

17. 1st
Activity:
Find anything in the classroom that will
indicate the following terms.

18. • 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

19. Basic Postulates
• Determination Postulates
• Intersection Postulates
• Separation Postulates

20. Determination Postulates
• Line determination
• Plane determination
• Space determination

21. Determination Postulate
Line determination:
At least two points determine a
line.

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

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

24. Intersection Postulates
• Line intersection
• Plane intersection
• Space intersection
• Line-space intersection

25. Line Intersection:
Line a
Line b
C

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

27. Plane Intersection
A
B

28. Intersection Postulate
Plane Intersection:
If two different planes intersect, their
intersection is a line.

29. Space Intersection
Plane h

30. Space Intersection
C
D

31. Space
Intersection
V

32. Intersection Postulate
Space Intersection:
If two different spaces intersect, then
their intersection is a point, a line or a plane.

33. Plane-Line Intersection
t
T
R

34. Plane-Line Intersection
B

35. 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.

36. 2nd
Activity:
Answer the following questions and
choose between a point, line, plane and
space.

37. What is the intersection of?
Two
rulers

38. What is the intersection of?
A wall
and a
ceiling

39. What is the intersection of?
Two
classrooms

40. What is the intersection of?
A
flagpole
on the
ground

41. What is the intersection of?
A
paper
and a
ballpen

42. Separation Postulates
• Line separation
• Plane separation
• Space separation

43. Line Separation
R
S
T
T

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

45. Plane Separation
A
B

46. Plane Separation
Plane p
A
B Plane o

47. Separation Postulates
Plane Separation:
A line separates a plane into half-
planes.

48. Space Separation

49. Space Separation

50. Separation Postulates
Space Separation:
A plane separates a space into two
half-spaces.

51. 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.

52. Keeping in mind the following undefined
terms in geometry, determining their
intersections and separations, how can
we apply it in real world situation?

53. As an ordinary Christian student, how can
you explain yourself from being a point
in this world to make a big space for
salvation?