Mathematics 8

Quarter 3
Self-Learning Module 1
Mathematical System
(Undefined Terms)
Mathematics Grade 8
Quarter 3 – Self-Learning Module 1: Mathematical System (Undefined Terms)
First Edition, 2020

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Mathematics 8
Quarter 3
Self-Learning Module 1
Mathematical System
(Undefined Terms)
Introductory Message

For the Facilitator:

Welcome to the Mathematics Grade 8 Self-Learning Module on Mathematical

System (Undefined Terms)!

This Self-Learning Module was collaboratively designed, developed and

reviewed by educators from the Schools Division Office of Pasig City headed by its
Officer-in-Charge Schools Division Superintendent, Ma. Evalou Concepcion A.
Agustin, in partnership with the City Government of Pasig through its mayor,
Honorable Victor Ma. Regis N. Sotto. The writers utilized the standards set by the K
to 12 Curriculum using the Most Essential Learning Competencies (MELC) in
developing this instructional resource.

This learning material hopes to engage the learners in guided and independent
learning activities at their own pace and time. Further, this also aims to help learners
acquire the needed 21st century skills especially the 5 Cs, namely: Communication,
Collaboration, Creativity, Critical Thinking, and Character while taking into
consideration their needs and circumstances.

In addition to the materials in the main text, you will also see this box in the
body of the self-learning module:

Notes to the Teacher

This contains helpful tips or strategies that
will help you in guiding the learners.

As a facilitator you are expected to orient the learners on how to use this self-
learning module. You also need to keep track of the learners' progress while allowing
them to manage their own learning. Moreover, you are expected to encourage and
assist the learners as they do the tasks included in the self-learning module.
 For the Learner:

Welcome to the Mathematics Grade 8 Self-Learning Module on Mathematical

System (Undefined Terms)!

This self-learning module was designed to provide you with fun and
meaningful opportunities for guided and independent learning at your own pace and
time. You will be enabled to process the contents of the learning material while being
an active learner.

This self-learning module has the following parts and corresponding icons:

Expectations - This points to the set of knowledge and skills

that you will learn after completing the module.

Pretest - This measures your prior knowledge about the lesson

at hand.

Recap - This part of the module provides a review of concepts

and skills that you already know about a previous lesson.

Lesson - This section discusses the topic in the self-learning

module.

Activities - This is a set of activities that you need to perform.

Wrap-Up - This section summarizes the concepts and

application of the lesson.

Valuing - This part integrates a desirable moral value in the

lesson.

Posttest - This measures how much you have learned from the
entire module.
 EXPECTATIONS

1. Describe a mathematical system.

2. Illustrate the need for an axiomatic structure of a mathematical

system in general, and particularly the undefined terms of
Geometry.

PRETEST

Directions. Identify what is being asked in each question. Write the letter of the
correct answer on a separate paper.
1. Which of the following best describes a mathematical system?

I. Axioms, Postulates & Theorems III. Defined Terms

II. Undefined Terms IV. Shapes

A. I only B. II only C. I, II & III D. I, II, III & IV

2. What are the undefined terms in Geometry?

A. Point, line, and plane

B. Axiom, postulate, and theorem

C. Bisector, betweenness, and midpoint

D. Parallel, perpendicular, and intersecting lines

3. Which of the following is a subset of a line with two endpoints?

A. Angle B. Line segment C. Midpoint D. Ray

4. Which of the following is accepted to be true without proof?

A. Axiom B. Definition C. Postulate D. Theorem

5. What do you call a statement that has become a rule because it’s been proven to
be true?
A. Axiom B. Definition C. Postulate D. Theorem
 RECAP
Classify Me!!!

Direction: Classify the following words that represent a line, point, and plane from
the given word bank.

blackboard ray of light piece of paper

table top top of a book corner of a room
laser electric wire tip of a pen

LESSON

In your Grade 7 lesson, you were introduced to the world of Geometry. Similar
to other fields of mathematics, Geometry also has a mathematical system that is
made up of undefined terms, defined terms, axioms/ postulates, and theorems. The
undefined terms are terms that cannot be defined because they can only be
described or illustrated. These undefined terms are the building blocks of defined
terms and axioms/postulates. Axioms or Postulates are statements accepted to be
true without proof. On the other hand, statements that are proven to be true using
definitions, axioms/ postulates, and derived using reasoning are called theorems.

Example 1:

The Mathematical System

Undefined Defined Axioms/

Terms Theorems
Terms Postulates

Point Coplanar Lines Two points The sum of the

are lines on the determine a line measures of the
Plane same plane interior angles of a
triangle is 180°

Line A+B+C=180°
Undefined Terms
Many geometric terms were defined using the undefined terms. Notice that
from the given definition of coplanar lines, the words line and plane were used. The
point, line, and plane are called undefined terms. We cannot define these terms
because they can only be described or illustrated.

POINT - It has no length or

width, but it indicates a
position or location. It is 𝑴 Point 𝑀
represented by a dot and
named using a capital letter.
LINE - It has infinite length, no
width, nor thickness. It
𝑩 𝑪 𝒏
extends infinitely in two 𝑨
opposite directions. It is 𝟑 POSSIBLE NAME OF
represented by a straight line THE LINE
⃡
Line 𝐴𝐵 or 𝐴𝐵
with two arrowheads. A line is
⃡
Line 𝐴𝐶 or 𝐴𝐶
named by two of its points
Line 𝐵𝐶 or ⃡𝐵𝐶
with a symbol ↔ written on
Line 𝑛 or Line 3
top of two letters. A line may
also be named by one small RAYS on Line 3
letter or a number. A line has Ray AB or 𝐴𝐵
its parts or subsets. Ray BC or 𝐵𝐶
SUBSETS of A LINE Ray BA or 𝐵𝐴
Ray is a part of a line that Ray CA or 𝐶𝐴
starts at one point and
SEGMENTS on Line 3
extends infinitely in a set ̅̅̅̅
Segment AB or 𝐴𝐵
direction. Segment BC or ̅̅̅̅
𝐵𝐶
Line Segment is a part of a segment AC or ̅̅̅̅
𝐴𝐶
line that made up of two
endpoints.

PLANE - It is a flat surface

extending infinitely in all
directions. A plane has
𝑷 R
infinite length, infinite width,
but has no thickness. It is 𝑺 𝑻
usually represented in Plane 𝑃𝑆𝑇
drawings by a four‐sided Plane R
figure. To name a plane you
can use a capital letter
written at the corner or using
three non-collinear points in
it.
Example 2: a) Using Figure A, name the given line in different ways.

A.
𝑨 𝑩 𝑪 𝑫

Solution: ⃡𝐴𝐵 , 𝐴𝐶
⃡ , ⃡𝐴𝐷 , ⃡𝐵𝐶 , ⃡𝐵𝐷 , ⃡𝐶𝐷 , ⃡𝐵𝐴, 𝐶𝐴
⃡ , ⃡𝐶𝐵, ⃡𝐷𝐵 , ⃡𝐷𝐶

b) Using Figure B, name the given plane in different ways.

B. 𝑿 M
𝒀
𝒁

Solution: Plane M, plane XYZ, plane XZY, plane YZX, plane YXZ, plane ZYX,
plane ZYX

Example 3: Draw and label a figure for each condition.

⃡
A. Point E lies on 𝐶𝐷

B. line t contains A and B but does not contain C.

C. Plane D and E intersect in l.

Solution:

A. Point E lies on ⃡𝐶𝐷

B. line t contains A and B but does not contain C.

𝑪
𝒕

𝑨 𝑩

C. Plane D and E intersect in l.

E
l
 ACTIVITIES

Analyze and answer the given questions. Use a separate sheet of paper in
answering the activities.

ACTIVITY 1: LET’S PRACTICE!

Direction: Name each figure.

𝑼

𝑫 𝑭 𝑷

1. ________________________________ 4. _______________________________

N
𝒁 𝑯

𝑰
2. _______________________________ 𝑱

H
𝑷
𝑸
𝑹 5. ______________________________

3. _______________________________

ACTIVITY 2: KEEP PRACTICING!

Direction: Use the figure at the right to answer what is being asked:

________1. How many planes are there in the figure?

________2. How many planes contain H?

________3. Name two lines that contain N.

________4. Name two points not on the Plane XBN.

________5. Name four points that are coplanar.
ACTIVITY 3: TEST YOURSELF!

Direction: Draw and label a figure for each condition.

1. Plane FGH

⃡ at M.
2. Line z intersecting 𝑇𝑄

3. Ray AB and Ray AM intersect at point A.

4. Plane H contains line 3 but does not contain Z.

⃡
5. Point W lies on 𝑆𝑇

WRAP-UP

Remember that…

The Mathematical System is consists of undefined terms, defined terms, axioms/

postulates, and theorems.
Undefined terms - are terms that cannot be defined because they can only be
described or illustrated. The three undefined terms are point, line, and plane.

Defined terms – are terms with a precise and concise definition.

Axioms or Postulates - are statements accepted to be true without proof.

Theorems – are statements that are proven to be true using definitions, axioms/
postulates, and derived using reasoning.
 VALUING

Reflections: (Journal Writing)

As a “New Normal Learner”, draw or name models of point, line, and a plane
that can be related or essential under “New Normal of Learnings” and explain their
importance. Use a separate sheet of paper.

POSTTEST

Directions: Identify what is being asked in each number. Write the letter of the
correct answer on your paper.

1. Which of the following does NOT describe a mathematical system?

A. Intersecting lines C. Theorems

B. Postulate and axioms D. Undefined and defined terms

2. What undefined term that has infinite length but with no width nor thickness?

A. Angle B. Line C. Plane D. Point

3. What does the edge of a box represent?

A. Line B. Plane C. Point D. Polygon

4. Which mathematical system does NOT require a definition but it is used as a basis

in defining other terms.

A. Defined terms C. Theorem
B. Postulate D. Undefined terms

5. The following are the possible names for the line illustrated below except_______.

𝑷
𝒕

𝑹 𝑺 𝑻

⃡
A. 𝑅𝑆 ⃡
B. 𝑆𝑇 ⃡
C. 𝑅𝑇 ⃡
D. 𝑅𝑃
 Chan Hong. New Syllabus Mathematics 8. Manila: Rex Book Store, Inc., 2016.
Yeo, Joseph, Seng, Teh Keng, Yee, Long Cheng, Chow, Ivy, Meng, Neo Chai, and Ong
Salesiana Books by Don Bosco Press Inc., 2018.
Nievera, Gladys. Grade 8 Mathematics: Patterns and Practicalities. Rev. ed. Makati:
Inc., 2015.
Mathematics for the 21st Century Learner 8. Makati: Diwa Learning System
Alagan, Robelyn, Bunag-Villafuerte, Esmeralda, Nazal, Rosalie, and Danilo Si.
Store, Inc., 2015.
Oronce, Orlando, and Marilyn Mendoza. E-Math 7. Rev. ed. Manila: Rex Book
References
MODULE 1
PRETEST
1. C 2. A 3. B 4. C 5D
RECAP
Line – Laser, ray of light, electric wire, corner of a room
Point – tip of a pen
Plane – blackboard, table top, top of a book, piece of paper
ACTIVITY I: LET’S PRACTICE!
⃡
1. line y or 𝐷𝐹
2. Z
3. answer may vary
(Plane H, plane PQR, plane QRP, plane RQP, plane PRQ, plane
QPR, plane RPQ)
⃡
4. 𝑈𝑃
5. answers may vary
(Plane N, plane HIJ, plane HJI, plane IJH, plane JIH, plane
JHI, plane IHJ)
ACTIVITY 2: KEEP PRACTICING!
1. 6 2. 4 3. 𝐻𝑁
⃡ , 𝐵𝑁
⃡ , 𝐽𝑇 ⃡
⃡ or 𝑇𝑁
4. J and T 5. H, B, N and X
ACTIVITY 3: TEST YOURSELF!
1-5 answers may vary
POSTTEST
1. A 2. B 3. A 4. D 5. D
KEY TO CORRECTION