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MATHEMATICS
Quarter 3 – Module 1
Introduction to Geometry

NegOr_Q3_Mathematics7_Module1_v2
Mathematics – Grade 7
Alternative Delivery Mode
Quarter 3 – Module 1: Introduction to Geometry

Second Edition, 2021

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Every effort has been exerted to locate and seek permission to use these materials from
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represent nor claim.

Published by the Department of Education

Secretary: Leonor Magtolis Briones
Undersecretary: Diosdado M. San Antonio

Development Team of the Module

Writer: ELENITA S. AMPALAYO
Editor: ROLANDO B. ABRASADO
Reviewer: ROLANDO B. ABRASADO
Illustrators:
Layout Artist: ANGELICA G. BAJAR
Management Team: Senen Priscillo P. Paulin, CESO V Elisa L. Baguio, Ed.D.

Joelyza M. Arcilla, EdD, CESE Rosela R. Abiera

Marcelo K. Palispis, JD, EdD Maricel S. Rasid

Nilita L. Ragay, Ed.D Elmar L. Cabrera

Inilimbag sa Pilipinas ng ________________________

Department of Education - Region VII Schools Division of Negros Oriental

Office Address: Kagawasan, Ave., Daro, Dumaguete City, Negros Oriental

Tel #: (035) 225 2376 / 541 1117
E-mail Address: negros.oriental@deped.gov.ph

NegOr_Q3_Mathematics7_Module1_v2
Introductory Message
This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue
your studies and learn while at home. Activities, questions, directions, exercises, and
discussions are carefully stated for you to understand each lesson.
Each SLM is composed of different parts. Each part shall guide you step-by-step as you
discover and understand the lesson prepared for you.
Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will
tell you if you need to proceed on completing this module or if you need to ask your
facilitator or your teacher’s assistance for better understanding of the lesson. At the end of
each module, you need to answer the post-test to self-check your learning. Answer keys are
provided for each activity and test. We trust that you will be honest in using these.
In addition to the material in the main text, Notes to the Teacher are also provided to our
facilitators and parents for strategies and reminders on how they can best help you on your
home-based learning.
Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use
a separate sheet of paper in answering the exercises and tests. And read the instructions
carefully before performing each task.
If you have any questions in using this SLM or any difficulty in answering the tasks in this
module, do not hesitate to consult your teacher or facilitator.
Thank you.

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This module was designed to provide you with fun and meaningful
opportunities for guided and independent learning at our own pace and time. It is
designed to help you in representing point, line, and plane using concrete and
pictorial models. Illustrate subsets of a line. Classifies different kind of angles.
In this learning module the students will learn to represents point, line and
plane using concrete and pictorial models and illustrates subsets of a line that
classifies different kinds of angles.

MODEL ANALYSIS

Questions:

1. What are the geometric figures can you observe in the picture above?
2. How do these figures form the scenery?
3. Why do you think points, lines, planes are considered the undefined terms in
Geometry?

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 ’s In

Geometry comes from the Greek words: geo, meaning “earth,” and metri meaning
“measurement.” Therefore, geometry means earth measurement. Geometry was first
developed by an ancient Greek philosopher named Euclid around 300 BCE. His book,
“Elements,” is used as a basic textbook in geometry.

’s New

Lesson
1
POINTS, LINES, PLANES

The Points, Lines, and Planes are called the undefined terms in Geometry because they are
the basis in forming other figures that you can see around. Without these three, other figures
will not be form. That is why Point, Line, Plane is important to study Geometry.

POINT LINE PLANE

Model

.E
. .
E A
●I
●N

●U
●C

With an arrowhead
How to draw as a dot at both ends

Two capital letters A capital letter

with points on the sometimes in cursive
How to name A capital letter line or a small letter form or three
noncollinear points

̅̅̅̅
𝐸𝐴 or ̅̅̅̅
𝐴𝐸 , line m, Plane R
line EA or line AE Plane NIU
Words/Symbols Point A Plane IUC
Plane NCU
Plane NIC
Plane NICU

It consists of A 2-dimensional
collinear points figure represented
Definition It is the basic unit in extended in both by a flat surface
Geometry and no sides infinitely and a extended in all
definite shape and 1-dimensional figure directions without
size. end.

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 ’s Is It

POINT. The basic unit in Geometry and mostly used to represent an object in an area.
Examples:

Screw earpiece control button

LINE. A one-dimensional figure with series of collinear points.

Examples:

Stick Rod charger wire Brake wire

PLANE. Plane is represented by a flat surface that extended to all directions infinitely.
It is a 2-dimensional figure.
EXAMPLES:

Stamp pad road computer screen

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 Identifying points, lines, and planes.

n E
●
M
●
L
●
Y
●J

1. Name two points on line n. List all three pairs of possible answers.

Answer: M and L, L and Y, M and Y

2. Give four names for the line. Write all possible answers.
Answer: line n, ̅̅̅̅
𝑀𝐿, ̅̅̅̅
𝐿𝑌 , ̅̅̅̅̅
𝑀𝑌

3. Give all the possible names for the plane shown above.
Answer: Plane E, Plane MLJ, Plane LYJ, Plane MYJ, Plane MLYJ

Let us proceed using the undefined terms.

Defined Term Model and Definition
Collinear Points
● ● ●
- These are points that lie on the same T A N m
line. Points T, A, and N are collinear because
they lie on line m.
Noncollinear Points n ●C
● ●
- These are points that do not lie on the H E
same line.
Points C, H, and E are noncollinear because
point C is not on line n.
Coplanar Points
S ●L
- These are points that lie on the same ●I
plane. ●O

Points O, I, and L are coplanar because they

lie on the same plane.
Noncoplanar Points
●Y
- These are points that do not lie on the ●B ●J ●T G
same plane.
Points Y, B, J, and T are noncoplanar
because point Y is not on plane G.
(Orlando A. Oronce and Marilyn O. Mendoza n.d.) NegOr_Q3_Mathematics7_Module1_v2
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 I Have Learned

Instruction: Make a journal to manifest your understanding about the topic. You can start it
by following the format below. Write it in your note book.

I have learned that collinear points are ___________________________

__________________________________________________________
_____________________________________________________ .

I have learned that noncollinear points are _______________________

_________________________________________________________
_______________________________________________________ .

I have learned that coplanar points are __________________________

_________________________________________________________
________________________________________________________ .

I have learned that noncoplanar points are ______________________

_________________________________________________________
_______________________________________________________ .

I Can Do

Determine the geometric figure suggested by each of the following as point, line, and plane.
1. A blackboard in your classroom
2. A table top
3. The tip of a pen
4. The corner of the room

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A. Determine what undefined term is being modelled by each picture.

1. _________________ 2. ________________ 3. _________________

4. __________________ 5. ________________ 6. ________________

B. Use the figure at the right. Identify each set of points as collinear, coplanar, noncollinear, or
noncoplanar.

7. C, G, A - __________ ___________ ● D
8. C, G, O, D - __________ ___________
9. D, G, R - ____________ ____________ C A
● ●
10. A, G, E, O - ____________ ____________
●G
●O E
●

●R

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Answer Key ( Lesson 1)
What I Know:
Nos. 1-3 Answer may vary
What I Can Do:
1. Plane
2. Plane
3. Point
4. Line
Assessment:
A. 1. Plane
2. Point
3. Line
4. Line
5. Point
6. Plane
B. 7. Noncolinear, coplanar
8. Noncolinear, noncoplanar
9. Noncolinear, noncoplanar
10. Noncolinear, coplanar
 Lesson
2 Subsets of a Line
Let us now study the key concepts on segments and rays.

LINE SEGMENT
Model
● ●
E J
How to Name Two capital letters with segment
symbol on top of the two letters
Words/Symbols Line segment EJ, ̅̅̅𝐸𝐽
Description It is a line with two endpoints at both sides.

RAY

Model A C
● ●
B G
● ●

How to Name Two capital letters with a ray symbol on

top.
Words/Symbols Rays AG and GB, ⃗⃗⃗⃗⃗
𝐴𝐶 , ⃗⃗⃗⃗⃗
𝐺𝐵

Notes: The end point of the symbol should

the correct letter from the figure. It does not
matter where the arrow facing, the endpoint
should be the letter without the arrow.
Description A ray is a line with an endpoint and an
arrow at the other side extended infinitely.

OPPOSITE RAYS

Model
C A R
● ● ●
Words/Symbols
⃗⃗⃗⃗⃗ and 𝑨𝑹
𝐴𝐶 ⃗⃗⃗⃗⃗⃗ are opposite rays with point A
as the common endpoint.
Description These are two collinear rays with common
endpoint.

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 BETWEENNESS

Model
● ● ●
J E G
Words/Symbols Point E is between Points J and G.
̅̅̅ + 𝐸𝐺
𝐸𝐽 ̅̅̅̅ = 𝐽𝐺
̅̅̅
Description A point is in between two points if and only
if the three points lie on the same line.

MIDPOINT of a SEGMENT

Model
● I ● I ●
T D S
Words/Symbols Point D is the midpoint of the line segment
TS. (Point D is in the middle of Points T
and S)
Description A point can be called midpoint if and only if
the points lie on the same line and the
distance between line segments are equal.
(The tick on the figure represents that the
line segments are in equal distance.)
(Orlando A. Oronce and Marilyn O. Mendoza n.d.)

’s More

Name the figure in different ways.

P Q R S
● ● ● ●

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 I Have Learned

Instruction: Make a journal to manifest your understanding about the topic. You can start it
by following the format below.

I have learned that a ray _______________________________________________________

___________________________________________________________________________
__________________________________________________________________________.
I have realized that a point can be called midpoint if _________________________________
___________________________________________________________________________
__________________________________________________________________________.

A. Refer to the figure below for numbers 1 – 3.

F A C E B
● ● ● ● ●

1. Name a pair of opposite rays. 2. Name ⃗⃗⃗⃗⃗

𝐸𝐹 in two other ways.

B. Refer to the figure below to find the length and coordinates of the following points.
I N S T A G M
● I ● I I ● I I ● I ●
2 4 7 10 12

3. The length of ̅̅̅

𝐼𝑇 ̅̅̅̅
4. The length of 𝑁𝐺
5. The coordinate of point S 6. The coordinate of point A
̅̅̅̅̅
7. The length of 𝑁𝑀 8. The length of ̅̅̅
𝐼𝐺

(Orlando A. Oronce and Marilyn O. Mendoza n.d.)

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Lesson
3
Angles

’s Is It

Angle. An angle is the union of noncollinear rays with a common endpoint.

Vertex. A vertex is the common endpoint of the two noncollinear rays.

Sides of the Angle. The two rays which make the sides of the angle.

Degrees. The unit for angle is degrees.

Protractor. The device used to measure angle is a protractor.

Vertex ● Angle

The three parts of an angle that separates it in a plane:

exterior ●
1. The interior
2. The exterior
Interior
3. The angle itself

Angle itself

Classification of Angles

Right Angle. A right-angle measures exactly 90°.

m∠𝐸 = 90°

E●
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 Acute Angle. An acute-angle measures less than 90°.

m∠L< 90°

L●

Obtuse Angle. It measures greater than 90° but less than 180°
.
90° < m∠A < 180°

●
A

Angles with the same measurements are congruent.

CONGRUENT ANGLES
Congruent angles are angles having equal measurements.

●A T
●

F 35° I 35° H
● ● ●

∠ AIF ≅ ∠ TIH (“Angle AIF is congruent to angle TIH”)

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ANGLE BISECTOR
The angle bisector is a ray having the common endpoint with the vertex of the angle.
Angle bisector can divide the angle into two congruent angles.

● ⃗⃗⃗⃗⃗
𝐿𝑉 is an angle bisector of
O angle OLE. Therefore, the
1 V two angles, ∠1 and ∠2, are
L● ● equal or congruent.
2
E
●

I Have Learned

Instruction: Make a journal to manifest your understanding about the topic. You can start it
by following the format below. Write it in your note book.

I have learned that congruent angles are ___________________________

____________________________________________________________
____________________________________________________________

I have realized that an angle bisector is ____________________________

____________________________________________________________
____________________________________________________________

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 I.
Refer to the figure below to answer each number.

O ●A
●
1 2 N
●
● ●
W M 3
S
●

1. Give the two other names of ∠1.

2. Name the two right angles.
3. Name a ray that bisects ∠AMS.
4. Name a pair of congruent angles.
5. ⃗⃗⃗⃗⃗⃗ as its side.
Name all angles that have 𝑀𝐴

Example 1. Refer to the figure at the right.

S ● V
●
a. Name a point in the interior
E
of ∠OPE. ● D
P ●
b. Name two angles that have R ● ●
S as vertex. O● ● N
c. List all angles that have E as
Vertex.
d. Name the 2 pairs of opposite rays.
e. List all angles that have ⃗⃗⃗⃗⃗
𝑅𝑃 as a side.
f. Is ∠R a valid name for one of the angles in the figure. Explain.

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Additional Activities:
Answers:
a. Point R
b. ∠RSO or ∠OSR and ∠VSO or ∠OSV
c. ∠REN or ∠NER and ∠VEN or ∠NEV
d. 𝑃𝐸
⃗⃗⃗⃗⃗ and 𝑃𝑁 ⃗⃗⃗⃗⃗ and ⃗⃗⃗⃗⃗
⃗⃗⃗⃗⃗⃗ , 𝐸𝑉 𝐸𝑅
e. ∠EPR, ∠RPO, ∠SRP, ∠NPR
f. Yes. Because it is the only one angle having R as a vertex.
References
n.d. Open High School Program. Grade 7Learning Modules - Mathematics. FAPE and Department of
Education.
Orlando A. Oronce and Marilyn O. Mendoza. n.d. e-math Geometry. 856 Nicanor Reyes Sr. St., Metro
Manila: Rex Book store.

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