Detailed Lesson Plan
Mathematics in the Modern World (GE04)
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DATE:
I. OBJECTIVES
II. SUBJECT
MATTER
III. PROCEDURE
A. DAILY
ROUTINE
February 14 – 18, 2021
At the end of the lesson the students should be able to:
 describe a mathematical system;
 define and illustrate a mathematical system;
 illustrates the need for an axiomatic structure of a mathematical system in general, and in
Geometry in particular: (a) defined terms; (b) undefined terms; and
 participate actively in class discussion
TOPIC: Mathematical System
SUB-TOPIC: Undefined and Defined Terms
REFERENCE: Mathematics Learning Module 8
MATERIALS: Laptop, WiFi, Cellphone, Earphone
1. Prayer and Greetings
2. Classroom Management
3. Checking of Attendance
WHAT IS GEOMETRY?
B. PREPARATORY
ACTIVITY
C. ACTIVITY
PROPER
Posing Questions:
1. What did the architect use in designing the buildings?
2. What did they consider in creating attractive patterns?
Geometry is the visual study of shapes, sizes, patterns, and positions. It occurred in all cultures,
through at least one of the five strands of human activities:
1. Building/structures
2. Machines/motion
3. Navigating/star-gazing
4. Art/patterns
5. Measurement
Mathematical System
 Mathematical system is divided into four parts namely undefined terms, defined, terms, axioms
or postulates and theorems.
 In geometry, we come across with terms which cannot be precisely defined and these are
undefined terms. The point, line, and plane are called undefined terms. We cannot define these
terms because they can only be described or illustrated.
 Unlike undefined terms (which do not have a formal definition), these terms have a formal
definition. They are used to define even more terms. Collinear points, coplanar points and
subsets of a line and more are called defined terms.
 A definition is an exact statement or description of the meaning of a term or word so that
anyone using it will understand it in the same way.
 Postulates on the other side is a statement which is accepted as true without proof. These
statements can be used as reasons in proving some mathematical statements.
 A theorem is a statement that can be proven. Once a theorem is proven, it can also be used as
a reason in proving other statements.
Undefined Terms
POINT indicates a position in
space. It has only location but
no dimension, length, width,
thickness and does not occupy
an area. It is named using a
CAPITAL LETTER and it can be
modeled by a dot.
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LINE has infinite length, no
width,
nor thickness.
It
extends infinitely in two
Point M
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POSSIBLE NAME OF THE
LINE

Line AB or 𝐴𝐵
opposite directions. It is
represented by a straight line
Line AC or 𝐴𝐶

Line BC or 𝐵𝐶
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with two arrowheads. A line is
named by two of its points with
a symbol ↔ written on top of
two letters. A line may also be
named by one small letter or a
number. A line has its parts or
subsets.
PLANE is a flat surface
extending infinitely in all
directions. A plane has infinite
length, infinite width, but has
no thickness. It is usually
represented in drawings by a
four‐sided figure. To name a
plane you can use a capital
letter written at the corner or
using three non-collinear points
in it.
Line 𝑛 or Line 3
Plane PST
Plane ℛ
Classify the following examples as points, lines or planes.
a. The top of your desk
b. The light from a laser pointer
c. The crease in a folded sheet of paper
d. The chocolate chips on a cookie
e. Bedroom walls
f. Stars in the sky
Examples: Using the figures below, name the given line in different ways.
 , 𝐹𝐸

𝐸𝐹
𝑅𝑆 , 𝑆𝑇
 , 𝑇𝑆, 𝑆𝑅 , 𝑅𝑇, 𝑇𝑅

Plane ABC, Plane 𝒫
Defined Terms
 In undefined terms, point, line and plane were established. Now, these terms will be used to
0 study of geometry.
define all other terms and0figures in the
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
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Figure 1
Collinear points are points that lie on the same line while non-collinear points are points that do
not lie on the same line.
Coplanar points are points that lie on the same plane while non-coplanar points are points that
do not lie on the same plane.
a. Points X, Y, Z are collinear points
b. Point A is non-collinear point
c. Point A, X, Y, and Z are coplanar points
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
Figure 2
Ray is a part of a line that starts at one point and extends infinitely in a set direction. It is
named with its endpoint first, followed by another point on the ray.
Ray AB or 𝐴𝐵
Ray BC or 𝐵𝐶
Ray BA or 𝐵𝐴
Ray CA or 𝐶𝐴
Opposite rays are rays with a common endpoint but extending in opposite directions
Common endpoint: B
 𝑎𝑛𝑑 𝐵𝐶
Opposite rays: 𝐵𝐴
Line Segment is a part of a line that made up of two endpoints.

Segment AB or 𝐴𝐵

Segment BC or 𝐵𝐶

Segment AC or 𝐴𝐶
Example: Draw and label a figure for each condition.

A. Point N lies on 𝑅𝑆
𝐑
𝐍
B. line u contains M and N but does not contain O.
𝐎
𝐌
C. Plane Y and Z intersect in k.
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𝐒
𝐍