This is the Mathematics Grade 4 Quarter 3 Module 1 self-learning module, “Kinds of Lines,” from DepEd Region V’s Alternative Delivery Mode series (First Edition, 2020). It is written for Grade 4 learners studying at home, with support from parents and teachers. After working through it, learners can tell apart parallel, intersecting, and perpendicular lines, describe them, and draw them.
On this page 6 sections
What learners will learn
After going through this module, learners are expected to be able to:
- Describe and draw parallel, intersecting, and perpendicular lines using a ruler and set square.
- Identify the different kinds of lines.
The three kinds of lines
The module opens with Neil, a pupil of Grade 4 Resourceful, who draws a house. His drawing has a fence, windows, and a door, and each part shows one kind of line. The module asks learners to look for lines in the drawing and to think about why lines matter, since we see lines in almost everything around us.
| Kind of line | Meaning | Example from Neil’s house |
|---|---|---|
| Parallel lines | Lines that do not intersect, even when extended in either direction | The horizontal lines of the fence, which never meet however far they are extended |
| Intersecting lines | Lines that meet or cross at a point | The two diagonal lines in the window, which cross to form an X |
| Perpendicular lines | Lines that intersect and form a right angle (90°) | The horizontal and vertical lines of the door, which cross at right angles |
How the module names and shows lines
The module labels lines with letters:
- Lines AB and CD are parallel. They will not meet no matter how far they are extended to the left or right.
- Line IL and line JK are intersecting lines. They cross at point M.
- Lines EF and GH are perpendicular. A small square at each corner where they cross shows that the angle is a right angle, or 90°.
A key idea is that every pair of perpendicular lines is also a pair of intersecting lines. Perpendicular lines are a special case because they meet at a right angle. The module also points out parallel lines in everyday shapes. For example, the opposite sides of a rectangle are parallel.
Activities in the module
- What I Know (pretest): Learners identify lines in four figures, draw one object for each kind of line, and describe each kind of line.
- Activity 1, “Name Us”: Learners name the kind of line described by each statement.
- Activity 2, “Explore the Space”: Learners find at least one pair each of parallel, intersecting, and perpendicular lines on a labeled grid.
- Activity 3, “Draw Me”: Learners draw two parts of their house with parallel lines, two objects in their bag with perpendicular lines, and two objects in the garden with intersecting lines.
- What I Can Do: Learners design a vegetable garden for their yard using the different kinds of lines.
- Assessment: Learners name pairs of lines from a figure, fill in definitions, and draw an example of each kind of line.
- Additional Activities: Learners use the kinds of lines to design a house that cannot easily be destroyed by a typhoon.
How to use this module
- Start with the pretest in What I Know, then check your answers on the last page. A score of 9 or 10 means you should have no difficulty with the lesson. A score of 8 or below means you should study the lesson carefully and do all the activities.
- Read What’s In, What’s New, and What is It in order. Use Neil’s house drawing to see each kind of line.
- Do the three activities in What’s More. Then review the summary in What I Have Learned.
- Finish with What I Can Do, the Assessment, and the Additional Activities.
For learners: Write your answers on a separate sheet of paper, not on the module. Have a ruler and set square ready for drawing. Use the answer key honestly to check your work.
For parents: Help your child spot parallel, intersecting, and perpendicular lines in things at home, such as windows, doors, and fences.
For teachers: The module includes an answer key for the pretest, the activities, and the assessment. The drawing tasks have answers that may vary.
Frequently asked questions
What grade and quarter is the Kinds of Lines module for?
It is Mathematics Grade 4, Quarter 3, Module 1, published as part of DepEd’s Alternative Delivery Mode in 2020.
What is the difference between intersecting and perpendicular lines?
Intersecting lines are lines that meet or cross at a point. Perpendicular lines are intersecting lines that form a right angle, which measures 90°.
What are parallel lines?
Parallel lines are lines that do not intersect, even when they are extended in either direction. The horizontal lines of a fence are an example.
Does the module have an answer key?
Yes. The last page has answers for the pretest, the What’s More activities, and the assessment. Answers to the drawing tasks may vary.
What tools do learners need for this module?
Learners need a separate sheet of paper for their answers. They also need a ruler and a set square, which the objectives say they will use to draw the lines.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 3 – Module 1: Kinds of Lines
4
[illustration: pupils and a teacher studying outdoors and indoors, with a globe, a lamp, and a student writing on paper]
CO_Q3_Mathematics 4_ Module 1
Mathematics – Grade 4 Alternative Delivery Mode Quarter 3 – Module 1: Kinds of Lines First Edition, 2020
Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as a condition the payment of royalties.
Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this module are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them.
Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio
Development Team of the Module
Writer: Elena D. Hubilla Editor: Loyd H. Botor Reviewer: Loyd H. Botor Illustrator: Jason C. Borabo Layout Artist: Cherry Lou O. Calison Management Team: Gilbert T. Sadsad, Francisco B. Bulalacao Jr., Grace U. Rabelas, Ma Leilani R. Lorico, Monserat D. Guemo, Florena M. Deuna
Printed in the Philippines by ________________________
Department of Education – Region V
Office Address : Regional Center Site, Rawis, Legazpi City, 4500 Telefax : 0917-178-1288 E-mail Address : region5@deped.gov.ph
4
Mathematics Quarter 3 – Module 1: Kinds of Lines
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.
What I Need to Know
This module was designed in order to help you learn the different kinds of lines. Lines can be seen in most objects.
In this lesson, you will learn about the three different kinds of lines. The learning activities will allow you to explore, discover and appreciate the different kinds of lines which can be seen in objects around us. You will also learn how to describe and illustrate the different kinds of lines.
After going through this module, you are expected to be able to:
- Describe and draw parallel, intersecting and perpendicular lines using a ruler and set square set.
- Identify the different kinds of lines.
What I Know
We need a sheet of paper for our next activities.
A. Identify the kind of lines shown in the figure. Fill in the blanks by writing parallel, intersecting, or perpendicular.
_____ 1. [illustration: two straight lines crossing each other to form an X]
_____ 2. [illustration: two parallel lines with arrowheads at both ends]
_____ 3. [illustration: two lines meeting at a right angle, marked with a square corner]
_____ 4. [illustration: a vertical line and a horizontal line crossing, with a small square at the crossing point]
B. Draw objects that show parallel, intersecting or perpendicular lines. (one object for each kind of lines)
C. Describe the following kinds of lines. a. parallel lines b. intersecting lines c. perpendicular lines
Look at the last page to check your answers.
CONGRATULATIONS! If you got a score of 9 or 10, you should not have any difficulty studying the lesson in this module.
If you got a score of 8 or below, you may need to study the lesson more carefully and do all the given activities.
Lesson 1: Kinds of Lines
What’s In
Each of the pupils of Grade 4 Resourceful was asked to draw a house. Neil presented his drawing to the class. Take a look at it.
[illustration: Neil’s line drawing of a house with a triangular roof, two square windows with diagonal crossing lines, a grid-patterned door, and two fence sections made of horizontal lines]
Do you see lines in Neil’s drawing? In what parts of the house do you see lines? Do you think we can draw houses without lines? Are lines important? Why?
We see lines in most of the things around us. We see different kinds of lines in almost everything. Today, we will talk about the three kinds of lines.
What’s New
Parallel Lines
Let us look at Neil’s drawing of the fence.
[illustration: a fence drawn as a block of many closely spaced horizontal lines]
Neil drew the fence using horizontal and vertical lines. The horizontal lines do not intersect even if we extend them. Likewise, the vertical lines do not intersect even if we extend them. These lines are said to be parallel lines.
Parallel lines are lines that do not intersect.
Lines AB and CD below are parallel lines. They will not intersect however long we extend them to the left or to the right.
[illustration: two horizontal lines with arrowheads at both ends; labels A and B at the upper left and upper right, labels C and D at the lower left and lower right]
Intersecting Lines
Let us now look at Neil’s drawing of the window of the house.
[illustration: a square with both diagonals drawn, forming an X]
The diagonal lines cross or intersect each other. They are thus called intersecting lines.
So, we say, “Intersecting lines are lines which intersect”.
Line IL and line JK below are intersecting lines. They intersect at point M.
[illustration: two intersecting lines IL and JK crossing at point M; labels I, K, J, L, M]
Let us now look at Neil’s drawing of the door of the house.
[illustration: Neil’s drawing of a door, a rectangle divided into a grid of horizontal and vertical lines]
Neil used horizontal and vertical lines to draw his door. The horizontal lines intersect the vertical lines. What kind of angle is formed by one of the horizontal lines and one of the vertical lines. If you answered, “right angle”, you are correct. Each pair of intersecting horizontal and vertical lines in Neil’s door form a right angle. Each of these pairs are then described as perpendicular lines.
And so we say, “Perpendicular lines are lines that intersect and form a right angle”.
Lines EF and GH below intersect and form right angles. They are therefore perpendicular. The four small squares at the corners tell us that the angles formed are right angles or that the measures of the angles is 90°.
[illustration: lines EF and GH intersecting to form four right angles; labels G, E, F, H, “right angle”, and 90° at each of the four corners]
What is It
How do the kinds of lines differ from one another? Take a close look at the examples.
Parallel lines – lines that do not intersect. The figures below show parallel lines.
[illustration: two parallel double-headed arrows with labels W, E (top) and K, B (bottom)]
[illustration: double-headed block arrow with labels A (top) and X (bottom)]
[illustration: rectangle with labels L (top), N (left), S (right), P (bottom)]
[illustration: circle containing two parallel arrows pointing to parallel lines]
Lines WE and KB are parallel
Side A and side X are parallel
Sides L and P are parallel. Line N and line S are also parallel
The lines to which the two arrows point are parallel
Intersecting lines – lines that meet or intersect at a point. The figures below show intersecting lines.
[illustration: circle with two crossing lines]
[illustration: two crossing lines with arrowheads at each end]
[illustration: grid of crossing lines]
Perpendicular lines – lines that intersect and form right angles (angles measuring 90°). The pictures below show perpendicular lines.
[illustration: horizontal and vertical arrowed lines crossing, with a right-angle mark]
[illustration: rectangle with a right-angle mark at the corner where two lines meet; arrows point to the mark]
[illustration: circle divided by perpendicular horizontal and vertical lines, with a right-angle mark and arrows pointing to it]
What’s More
Activity 1 – “Name Us”
Name the pair of lines being described by each statement.
- We are lines that intersect each other.
- We are lines that intersect and form a right angle.
- We are lines which do not meet or intersect even when extended.
Activity 2 – “Explore the Space”
Look at the grid below and give at least 1 pair of parallel lines, 1 pair of intersecting lines, and 1 pair of perpendicular lines.
[illustration: grid with a horizontal line labeled X (left) and P (right), a horizontal line labeled R (left) and O (right), a vertical line labeled L (top) and M (bottom), and a diagonal line with arrow labeled A (lower left) and Z (upper right)]
Activity 3 – “Draw Me”
- Draw 2 parts of your house which show parallel lines.
- Draw 2 objects in your bag which show perpendicular lines.
- Draw 2 objects in the garden which show intersecting lines.
What I Have Learned
Let us remember:
- Parallel lines are lines that do not intersect even when extended in either direction.
- Intersecting lines are lines that intersect.
- Perpendicular lines are lines that intersect and form a right angle.
What I Can Do
Using the different kinds of lines, design a vegetable garden that you can put up in your yard.
Assessment
A. From the figure below, name 2 pairs of intersecting lines, 1 pair of parallel lines, and 2 pairs of perpendicular lines.
[illustration: two horizontal parallel lines with arrowheads labeled L (top left), S (top right, on a slanted transversal), Q (left), W (right), E (bottom left), T (bottom right), K (bottom, on a vertical line), P (bottom, on the slanted line); right-angle marks where the vertical line meets the horizontal lines]
B. Fill in the blanks with the kind of lines being described.
- _____________________ are lines that intersect at a point.
- _____________________ are lines that do not intersect even if they are extended in either direction.
- _____________________ are lines that intersect and form right angles.
C. Draw an example of each kind of lines.
- Intersecting lines
- Perpendicular lines
- Parallel lines
Additional Activities
Using the different kinds of lines, make a design of a house that cannot be easily destroyed by a typhoon.
[transcriber’s note: this page is printed upside down; it is transcribed upright in reading order]
Answer Key
What I Know
A. 1. Intersecting lines 2. Parallel lines 3. Perpendicular lines 4. Perpendicular lines
B. (drawings may vary)
C. a. Parallel lines are lines which will not intersect even when extended in either direction. b. Intersecting lines are lines which intersect at a point. c. Perpendicular lines are lines which form right angles.
What’s More
Activity 1
- Parallel lines
- Perpendicular lines
- Intersecting lines
Activity 2
- Parallel lines
- lines XP and RO
- Perpendicular lines
- lines LM and XP
- lines LM and RO
- Intersecting lines
- lines LM and ZA
Activity 3
parts of the house with these lines
[illustration: two parallel double-headed lines]
objects with these lines
[illustration: a plus-shaped pair of perpendicular lines with arrowheads]
objects with these lines
[illustration: two crossing lines with arrowheads]
Assessment
A.
- Intersecting lines
- lines QW and SP
- lines ET and SP
- Parallel lines
- lines QW and ET
- Perpendicular lines
- lines LK and QW
- lines ET and LK
B.
- Intersecting lines
- Parallel lines
- Perpendicular lines
C.
- [illustration: two crossing lines with arrowheads]
- [illustration: perpendicular lines with arrowheads]
- [illustration: parallel lines with arrowheads]
References
Electronic Sources:
Cue Math, The Math Experts. “Types of Lines in Math”. https://www.cuemath.com/learn/types-of-lines/
Department of Education. “DepEd Order No. 12, s. 2020. Adoption of the Basic Education Learning Continuity Plan for SY 2020-2021 In Light of the Covid-19 Public Health Emergency”. Accessed June 19, 2020. p. 342. https://www.deped.gov.ph/2020/06/19/june-19-2020-do012-2020-adoption-of-the-basic-education-learningcontinuity-plan-for-school-year-2020-2021-in-the-light-ofthe-covid-19-public-health-emergency/
For inquiries or feedback, please write or call:
Department of Education – Bureau of Learning Resources (DepEd-BLR)
Ground Floor, Bonifacio Bldg., DepEd Complex Meralco Avenue, Pasig City, Philippines 1600
Telefax: (632) 8634-1072; 8634-1054; 8631-4985
Email Address: blr.lrqad@deped.gov.ph * blr.lrpd@deped.gov.ph
Leave a Reply