The document outlines the components of an axiomatic structure in mathematics, specifically in geometry, including defined and undefined terms, postulates, and theorems. It includes several activities that engage learners in identifying geometric concepts and justifying statements about figures using postulates and theorems. The objective is to illustrate the importance of such a structure for understanding geometry.

1. Learning Competency:
illustrates the need for an axiomatic
structure of a mathematical system in
general, and in Geometry in particular:
(a) defined terms;
(b) undefined terms; (c)postulates; and
(d) theorems.

2. Objectives:
illustrates the need for an axiomatic structure
of a mathematical system in general, and in
Geometry in particular:
(a) defined terms
(b) undefined terms

7. Activity 1: Identify Me!
Determine whether the object is a point, line, or
plane.

8. Answers

9. Activity 2: Tell Me!

10. Check your answer

11. UNDEFINED TERMS

12. UNDEFINED TERMS

13. UN DEFINED TERMS

14. DEFINED TERMS

15. DEFINED TERMS

17. Activity 3: Name Me!

18. Answers

19. Individual Work

20. Answer

21. Activity 4

22. Answers

27. Theorem

28. Theorem

29. Theorem

31. Test yourself!
State the postulate or theorem you would use to justify the
statement made about each figure.
Answer: Through any
three non- collinear
points, there is exactly
one plane.
( Postulate 4)

32. Test yourself!
State the postulate or theorem you would use to justify the
statement made about each figure.
Answer: Through any
two points there is
exactly one line
( Postulate 3)

33. Test yourself!
State the postulate or theorem you would use to justify the
statement made about each figure.
Answer: If two points
lie in the plane, then
the line joining them
lies in that plane.
(Postulate 5)

34. Test yourself!
State the postulate or theorem you would use to justify the
statement made about each figure.
Answer: If two planes
intersect, then their
intersection is a line.
(Postulate 6)

35. Test yourself!
State the postulate or theorem you would use to justify the
statement made about each figure.
Answer: A line contains
at least two points.
(Postulate 1)

36. Test yourself!
State the postulate or theorem you would use to justify the
statement made about each figure.
Answer: If two lines
intersect, then exactly one
plane contains both lines.
(Theorem3)

37. Test yourself!
State the postulate or theorem you would use to justify the
statement made about each figure.
Answer: If a point lies
outside a line, then exactly
one plane contains both
the line and the point.
(Theorem2)

38. Test yourself!
State the postulate or theorem you would use to justify the
statement made about each figure.
Answer: If two lines
intersect, then they
intersect in exactly one
point. (Theorem1)

39. Activity 1: AGREE OR DISAGREE

40. Answers

41. Activity 2: Answer Me Please!

42. Answers