Mathematical System Undefined

1. LET’S OBSERVE!
write in your
notebook 5 things
that you can observe
around the
classroom.

2. LET’S OBSERVE!
1. How did you come
up with your
observation?
2. Is your observation
valid? Why or why

3. MATHEMATI
CAL
SYSTEM

4. Objectives:
AT THE END OF THE LESSON, THE LEARNERS SHOULD
BE ABLE TO:
a. Describes a mathematical system
b. Determine a mathematical system
in a statement; and
c. Relate mathematical system into
real life situation.

5. “Lets Observe! ”
Direction: From your learning in geometry in
your previous grade, write something about the
following terms.
1. Point
________________________________________________________
2. Line
________________________________________________________
3. Plane
________________________________________________________

6. 1. How do you define each term?
2. Why does the three term is important in
mathematics?

7. POINT
FIGURE
•A
DESCRIPTION
A point suggests an exact
location in space. It has no
dimension. We use a
capital letter to name a
point.
NOTATION
point
A

8. LINE
FIGURE
DESCRIPTION
A line is a set of points arranged in a
row. It is extended endlessly in both
directions.
It is a one-dimensional figure. Two
points determine a line. That is, two
distinct points are contained by exactly
one line. We use a lower case letter or
any two points on the line to name the
line.
NOTATION
line m
or (RV)

9. PLANE
FIGURE
DESCRIPTION
A plane is a set of points in an endless flat
surface.
The following determine a plane:
(a) three non-collinear points;
(b) two intersecting lines;
(c) two parallel lines; or
(d) a line and a point not on the line. We
use a lower case letter or three points on
the plane to name the plane.
NOTATION
plane PQR
or PQR

10. Angles
An angle is a union of two non-collinear rays with
common endpoint. The two non-collinear rays are the
sides of the angle while the common endpoint is the
vertex.

11. LINE SEGMENT
A line segment is a part of a line that has two endpoints. We define a line segment AB as a subset of
line AB consisting of the points A and B and all the points between them. If the line to which line
segment belongs is given a scale so that it turns into the real line, then the length of the segment
can be determined by getting the distance between its endpoint.
RAY
A ray is also a part of a line but has only one endpoint, and extends endlessly in one direction. We name a
ray by its endpoint. The figure is ray AB or we can also name it as ray AC. It is not correct to name it as ray
BA or ray CA.In notation, we write AB or AC.

12. AXIOMS
Axiom is a concept in logic, a statement which is accepted without
question and which does not require proof.
There are reasons why it has no proof for example:
1. The statement might be obvious. This means most people think it is
clearly
true.
2. The statement is based on physical laws and can easily be observed.
3. The statement is a proposition.

13. AXIOMS
Principle of Contradiction is an example of an obvious axiom. It
says that a statement and its opposite cannot both be true at the
same time and place. Thus, you can have a contradictory
statement.
Example of a contradictory statement:
“banal na aso”
“the cleanest mess”
“the sweetest salt”

14. What is a
Theorem?
A theorem is a statement that can be
demonstrated to be true by accepted
mathematical operations and arguments. In
general, a theorem is an embodiment of some
general principle that makes it part of a larger
theory.

15. THEORE
MS
Example:
Formula:
a² + b² = c²
a = side of right triangle
b = side of right triangle
c = hypotenuse
This theorem states that the area of the triangle whose side is the hypotenuse
is equal to the sum of the areas of the squares on the other two sides.It is a
fundamental relation in Euclidean geometry among the three sides of a right
triangle.

16. Find the Angle, Line Segment, & Rays!
Direction: Name at least 2 examples of each of the
following terms below from figure 2.
ILLUSTRATIVE EXAMPLE FROM FIG. 1: 1. Angle: ______ _______
Angle: LRQS 2. Line segment: _______ ______
Line segment: (QR) 3. Ray: ______ _______
Ray: (QS)

17. 1. How do you represent a point? a
line? and a plane??
2. Cite some real-world objects
illustrating a point, a line and a plane.

18. “ANSWER ME!”
Direction: Direction: Read each statement carefully and determine whether it is an
axiom (a fundamental truth accepted without proof) or a theorem (a statement proven
true based on axioms and other theorems). Write "A" for axiom and "T" for theorem
next to each statement.
______ 1.ALL PIZZAS ARE CIRCULAR.
______ 2.OPPOSITE SIDES OF A RECTANGLE ARE PARALLEL.
______ 3.WATER BOILS AT 100°C AT SEA LEVEL.
______ 4.THE SUM OF THE ANGLES IN A TRIANGLE IS 180°.
______ 5.TIME TRAVEL IS IMPOSSIBLE.
______ 6. TWO LINES WITH THE SAME SLOPE ARE PARALLEL.
______ 7. ADDING THE SAME NUMBER TO BOTH SIDES OF AN EQUATION
KEEPS THE
EQUATION BALANCED.
______ 8. EVERY EVEN NUMBER IS DIVISIBLE BY 2.
______ 9. THE SHORTEST DISTANCE BETWEEN TWO POINTS IS A STRAIGHT
LINE.

19. “Let’s Draw!”
DIRECTIONS: DRAW 5 OBJECTS THAT COULD REPRESENT EACH
OF THE FOLLOWING TERMS BELOW THAT ARE FOUND IN YOUR
HOME.
a. a point.
b. a line
c. a plane.

20. 1. What is the importance of
MATHEMATICAL SYSTEM in our life?
2. Can you think of other situations in
your daily life where MATHEMATICS
SYSTEM is used?

21. ANSWER ME!
Direction: In your notebook, select the best answer in the choices.
1. Which of the following represents a plane?
a. wire b. wall c. ball pen d. dot
2. A blackboard and floor represents what?
a. Plane b. Point c. ray d. line
3. It is a subset of a line that has two endpoints.
a. Skew lines b. Parallel lines c. ray d. line segment
4. The following represents a point EXCEPT.
a. tip of a pen b. a dot c. electric wire d. edge of a table
5. Line segment and ray are some of the examples of what?
a. undefined terms c. postulate
b. defined terms d. theorem.

22. Assignment: ½ Crosswise(10
pts)
1. Cite the difference between
an axiom/postulate and a
theorem.