This self-learning module is Mathematics Grade 5, Quarter 3, Module 9: Identify the Terms Related to a Circle. It was developed by DepEd Region VIII (First Edition, 2020) for learners studying at home through Alternative Delivery Mode. After working through it, learners should be able to name and recognize the parts of a circle, from the center and radius to arcs, angles, and tangent lines.
The module starts from things learners already know. Coins, plates, wheels, and clocks are all circular, and the terms in this module help describe them.
On this page 6 sections
What learners will learn
The module states one learning objective. After going through it, learners are expected to:
- Identify the terms related to a circle.
Key terms related to a circle
The module defines a circle as the set of all points on a plane that are the same distance from a fixed point called the center. A point is inside, on, or outside a circle depending on whether its distance from the center is less than, equal to, or greater than the length of a radius.
A circle is named by its center. If the center is point A, the figure is called circle A.
| Term | Meaning in the module |
|---|---|
| Center | The fixed point that all points on the circle are the same distance from |
| Chord | A line segment joining any two points on the circle |
| Diameter | A chord that passes through the center; every diameter is a chord |
| Radius (plural: radii) | A line segment from the center to a point on the circle; it is one-half of the diameter |
| Central angle | An angle formed by two radii |
| Inscribed angle | An angle whose vertex is on the circle |
| Arc | A part of the circle |
| Semicircle | An arc that is half of the circle |
| Minor arc | An arc that is less than a semicircle |
| Major arc | An arc that is more than a semicircle |
| Tangent line | A line that touches the circle at exactly one point |
| Point of tangency | The point where the tangent line and the circle meet |
| Secant line | A line that crosses the circle at two points |
| Concentric circles | Circles that share the same center point |
Tips for telling the terms apart
- Chord, diameter, and radius. A chord connects two points on the circle. If that chord passes through the center, it is a diameter. A radius goes only from the center to the circle, so it is half as long as a diameter.
- Central and inscribed angles. Look at where the vertex (the corner of the angle) is. If it is at the center, it is a central angle. If it is on the circle itself, it is an inscribed angle.
- Arcs. Compare the arc with half the circle. Less than half is a minor arc, exactly half is a semicircle, and more than half is a major arc. The module names a minor arc with two letters (such as arc BG) and a major arc or semicircle with three letters (such as arc BFG).
- Tangent and secant lines. A tangent line touches the circle once. A secant line cuts through it at two points, so it contains a chord.
Parts of the module
- What I Know: a 10-item multiple-choice pretest on the circle terms.
- What’s In: a matching activity on everyday circular objects, such as a wheel, plates, a wall clock, a frying pan, and a Php 10 coin.
- What’s New and What is It: the discussion of the circle and its parts, with labeled figures.
- What’s More: four practice activities. In “What’s My Name”, “Name Me”, and “Identify Me”, learners name parts of a labeled circle. In “Match-Up”, they match parts to their names.
- What I Have Learned: Activity 5, where learners choose the correct term for each definition.
- What I Can Do: Activity 6, “Hunt Me”, a word search with ten circle words such as RADII, CHORD, ARC, and DIAMETER.
- Assessment: a 10-item multiple-choice post-test.
- Additional Activities: naming the center, radii, diameter, central angles, chords, and arcs of circle B.
- Answer Key: answers for the tests and activities.
How to use this module
For learners: Take the pretest first. If you get 9 or 10, you should have no trouble with the lesson. If you get 8 or below, study the lesson carefully and do all the activities. Read each definition in “What is It” while looking at its figure. Then do the activities in order and finish with the post-test. Write all answers on a separate sheet of paper, and do not mark the module. If you score below 9 on the post-test, go over the lesson and exercises again.
For parents: Help your child find circular objects at home, such as plates, coins, and clocks. Remind them to use the answer key honestly, only after answering.
For teachers: The labeled figures and naming activities show quickly whether learners can tell chords, diameters, and radii apart, and central angles from inscribed angles. Note that the pretest and post-test also ask about circumference (the distance around the circle) and the number of degrees in a circle, which the discussion does not explain. You may want to cover these briefly.
Frequently asked questions
What grade and quarter is this module for?
It is for Grade 5 Mathematics, Quarter 3. It is Module 9, titled Identify the Terms Related to a Circle.
Does the module have an answer key?
Yes. The module includes answer keys for the activities, the post-test, and the additional activities. Learners are asked to use them honestly after answering.
What is the difference between a chord and a diameter?
A chord is any line segment joining two points on the circle. A diameter is a chord that also passes through the center, so every diameter is a chord.
How is a radius related to the diameter?
A radius goes from the center to a point on the circle, and it is one-half of the diameter. The plural of radius is radii.
What are concentric circles?
Concentric circles are two or more circles that share the same center point.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 3 – Module 9: Identify the Terms Related to a Circle
5
[illustration: students reading and studying outdoors and at a table, with a teacher, a globe, and a lantern; ALTERNATIVE DELIVERY MODE logo below]
CO_Q3_Mathematics 5_ Module 9
Mathematics – Grade 5 Alternative Delivery Mode Quarter 3 – Module 9: Identify the Terms Related to a Circle 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
Writers: Ma. Alma Galitan and Danilo S. Jadulco
Editors: Norman E. Sagayap, Gina P. Diloy
Reviewers: Renato S. Cagomoc, Rolando Lacbo, Joshua Sherwin T. Lim
Layout Artist: Razle L. Jabelo, Maelyne L. Yambao
Management Team: Ma. Gemma M. Ledesma
- Arnulfo B. Balane
- Rosemarie M. Guino
- Joy B. Bihag
- Ryan R. Tiu
- Sarah S. Cabaluna
- Thelma Cabadasan-Quitalig
- Elena S. De Luna
- Renato S. Cagomoc
- Noel E. Sagayap
- Geraldine P. Sumbise,
- Joshua Sherwin T. Lim
Printed in the Philippines by _______________________
Department of Education – Region VIII
Office Address: Deped Regional Office No. 8, Candahug, Palo, Leyte Telefax: (053)-832-2997 E-mail Address: region8@deped.gov.ph
Mathematics Quarter 3 – Module 9: Identify the Terms Related to a Circle
5
[transcriber’s note: this page repeats the cover title and logo; the cover text above is transcribed once]
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
A lot of objects around us are circular in shape such as coins, plates, and wheels. This module is essential for you to understand the terms related to a circle. These terms are easy to remember and very useful in our daily life.
After going through this module, you are expected to:
- Identify the terms related to a circle.
What I Know
Good day to you! This part of the module aims to find out how much you know about the contents of this module.
Multiple Choice
Directions: Read each item carefully. Choose the letter of the correct answer and write it on a separate answer sheet.
What is a line segment joining any two points on the circle?
a. chord
b. center
c. diameter
d. radiusWhich of the following parts of a circle measures less than a semi-circle?
a. minor arc
b. major arc
c. inscribed angle
d. central angleWhat do you call a chord that passes through the center of the circle?
a. diameter
b. circumference
c. radius
d. arcWhich refers to the distance around the circle?
a. perimeter
b. circumference
c. diameter
d. central angleWhat is a line segment that connects the center and any point on the circle?
a. arc
b. chord
c. radius
d. diameterWhat do you call two or more circles sharing the same center?
a. equal
b. congruent
c. similar
d. concentricWhat is half of a circle?
a. Arc
b. semicircle
c. central angle
d. major arcWhich part of a circle measures more than 180 º?
a. diameter
b. semicircle
c. minor arc
d. major arcWhat do you call the intersection of the circle and tangent line?
a. diameter
b. point of tangency
c. radius
d. centerWhich line contains a chord of a circle?
a. tangent line
b. diameter
c. secant line
d. radius
Please check your answers against the ANSWER KEY on page 10.
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: Identify the Terms Related to a Circle
What’s In
There are many circular objects around us. Can you identify them? An object’s shape meets a specific purpose. Can you tell why the rim of a cup is a circle, why plugs and manhole covers are round or why the bottoms of pans are circular?
Directions: Identify circular objects in the real world by matching the object in column A to its name in column B. Writer the letter of your answer on a separate answer sheet.
| A | B |
|---|---|
| 1. [illustration: wheel] | a. Php 10 coin |
| 2. [illustration: stack of plates] | b. plate |
| 3. [illustration: wall clock] | c. cymbals |
| 4. [illustration: frying pan] | d. wall clock |
| 5. [illustration: Php 10 coin] | e. frying pan |
| f. wheel |
[transcriber’s note: the B items are printed beside the A pictures in the order a to f; the rows above follow that printed order and do not show a confirmed pairing]
What’s New
A circle is one of the most familiar geometric figures. All around us are circular objects such as coins, wheels, watches, plates, balls and the like. A circle’s symmetric properties make it a popular choice in architecture and design.
This module will focus on the different parts of the circle.
What is It
A circle is the set of all points that are the same distance from a fixed point on a plane called the center. A point is inside, on, or outside of a circle depending on whether its distance from the center is less than, equal to, or greater than the length of a radius, respectively.
Terms Related to a Circle
Point A is the center of the circle. A circle is named by its center. The circle in figure 1 is named circle A.
[illustration: Figure 1, circle with center A and chords through labeled points C, E, B, and D]
Figure 1
A line segment joining two points on the circle is called a chord. In Figure 1, $\overline{CE}$ and $\overline{BG}$ are chords.
A diameter of a circle is a chord that connects two points on the circle and passes through the center of the circle. Every diameter is a chord. In Figure 2, $\overline{BF}$ is a diameter.
[illustration: Figure 2, circle with center A and diameter from B to F]
Figure 2
A radius is a line segment from the center of the circle to a point on the circle. A radius of the circle is one-half of the diameter. In Figure 3, $\overline{AF}$, $\overline{AB}$, $\overline{AH}$ and $\overline{AD}$ are radii (plural form of radius).
[illustration: Figure 3, circle with center A and radii to labeled points D, B, F, and H]
Figure 3
A chord is a line segment joining any two points on the circle. In figure 3, 𝑫𝑯̅̅̅̅̅ and 𝑩𝑭̅̅̅̅ are chords. A diameter is a chord.
A central angle is an angle formed by two radii. In figure 4, ∠BAD, ∠BAH, ∠HAF, and ∠DAF are central angles.
Figure 4
[illustration: circle with center A and points B, D, F, H labeled; diameters DH and BF drawn]
An inscribed angle is an angle whose vertex is on the circle. In figure 5, ∠FBG is an inscribed angle.
Figure 5
[illustration: circle with center A and points B, C, E, F, G, H labeled; line BH and line CE drawn]
An arc is a part of the circle. In figure 5, you can find arc BG (in symbol 𝑩𝑮̂), arc BF, arc FG, and arc BFG.
A semicircle is an arc which is half of the circle. In figure 5, 𝐵𝐺𝐹̂ is a semicircle.
A minor arc is an arc that is less than a semi-circle. In figure 5, 𝐹𝐺̂ and 𝐵𝐺̂ are minor arcs.
A major arc is an arc that is more than a semi-circle. In figure 5, arc BFG and arc FBG are major arcs.
A tangent line is a line that intersects the circle at exactly one point. The point where the circle and tangent line intersect is called the point of tangency. In figure 5, line CE is a tangent line. Point F is the point of tangency.
A secant line is a line that intersects the circle at two points. In figure 5, line BH is a secant line.
Concentric circles are circles having the same center point. Figure 6 shows two concentric circles.
Figure 6
[illustration: two concentric circles with center labeled O; labels “Circle 1” (inner ring area) and “Circle 2” (outer ring area)]
Did you understand now? Very good.
Now, you are ready to do the activity below
What’s More
Let’s enhance your understanding of the parts of the circle by doing the next activity.
Activity 1: What’s My Name
Directions: Read each question carefully. Name the following based on the figure at the right.
- center
- 4 radii
- 2 diameters
- 3 chords
- 2 inscribed angles
[illustration: circle with center O; points A (top), B (bottom), C (left), D (right) on the circle; chords and diameters drawn between them]
Activity 2 Name Me
Directions: Name the following parts of circle P. Write your answer on a separate answer sheet.
- 3 radii
- diameter
- 3 chords
- 2 central angles
- tangent line
- secant line
- 2 inscribed angles
[illustration: circle P with points labeled R, Q, S, N, Y, T, X, and center P; line through X and T drawn as a tangent-style line; lines drawn between points]
Activity 3 Identify Me
Directions: Identify the following parts of Circle O. Write your answer on a separate answer sheet.
- OX
- BC
- Pt. B
- Pt. O
- AMY
- MOA
- AM
[illustration: circle O with points A, B, C, M, X, Y; center O; line through B and A; line BC drawn with arrowheads]
Activity 4 Match – Up
Directions: Refer to the figure shown. Match the parts of Circle O in Column A with the name of each part in Column B. Write your answer on a separate answer sheet.
| Column A | Column B |
|---|---|
| 1) Point A | a. center |
| 2) AD, BC | b. radius |
| 3) AB, AC, BD, CD | c. diameter |
| 4) ∠ABD, ∠BAC, ∠ACD, ∠BDC | d. chord |
| 5) ∠AOC, ∠COD, ∠BOD, ∠AOB | e. inscribed angle |
| 6) AE | f. point of tangency |
| 7) OB, OC, OA, OD | g. central angle |
| h. tangent line |
[illustration: circle O with points A (top), B (left), C (right), D (bottom), center O; line through A labeled E with arrowheads; chords and radii drawn]
What I Have Learned
Activity 5 Identify Me
Directions: Choose the correct answer from the words inside the box and write your answers on a separate sheet.
Circle, Radius, Diameter, Tangent line, Secant, Center, Inscribed angle, Chord, Central angle
_________1) It is the set of all points in a plane with the same distance from a certain point. _________2) It is a line segment joining two points on the circle. _________3) It is a chord that connects two points on the circle and passes through the center of the circle. _________4) It is a line segment from the center of the circle to any point on the circle. _________5) It is an angle formed by two radii.
What I Can Do
Activity 6 Hunt Me
Directions: Copy the puzzle below on your answer sheet. Encircle the 10 words that are related to circle. The words may be written horizontally, vertically or diagonally. Find the words that are shown inside the box.
CIRCLE, RADII, INSCRIBED, CHORD, ANGLE, ARC, MINOR, MAJOR, POINT, DIAMETER
I A A R A D I I S V A R C
N L N M N A B C D R X Y I
S P G L I N E I G O B X R
C O L C B N E U E J C N C
R I E A T X O L C A N I L
I N I E B S C R D M E N E
B T R D I A M E T E R R E
E E A A I N M I I T T T X
D A S C R X C H O R D A H
E B C A S T N M S Y X I N
Assessment
Multiple Choice
Directions: Read each item carefully. Choose the letter of the correct answer and write it on a separate answer sheet.
What part of a circle measures more than half a circle?
a. diameter
b. major arc
c. 3minor arch
d. semicircleWhat do you call the intersection of a circle and the tangent line?
a. Center
b. point of tangency
c. radius
d. arcHow many degrees are in a circle?
a. 90o
b. 180o
c. 270o
d. 360oWhich refers to the distance around the circle?
a. central angle
b. circumference
c. diameter
d. perimeter
Got a score of 9-10? CONGRATULATIONS! Job well done. See you in the next module. If you scored below 9, you may have to go over the lessons and the exercises again.
Please check your answers with the ANSWER KEY on page 10.
Which do you call two or more circles sharing the same center?
a. equal
b. congruent
c. similar
d. concentricWhat is a line segment that connects the center and any point on the circle?
a. arc
b. chord
c. radius
d. diameterWhat is half of a circle?
a. arc
b. semicircle
c. major arc
d. central angleWhat is a line segment that joints any two points on the circle?
a. chord
b. center
c. diameter
d. circumferenceWhich of the following measures less than a semicircle?
a. center
b. major arc
c. minor arc
d. tangent lineWhat do you call a chord that passes through the center of the circle?
a. arc
b. radius
c. diameter
d. circmference
Please check your answers with the ANSWER KEY on page 10.
Additional Activities
Answer this activity as an additional exercise.
Directions: Identify the following parts of circle B answer and write it on a separate answer sheet.
a. center: _____________ b. 4 radii: _____________ c. diameter: ___________ d. 4 central angles: ______________ e. 3 chords: __________ f. 2 minor arcs g. 2 major arcs
[illustration: circle B with center B, points C, D, N, M, O, P, Q; chords DN, OM, CP, OQ drawn; line through B to P]
Answer Key
[transcriber’s note: this page is printed rotated 180 degrees. The two columns below follow the order in which they read on the page: left column first, then right column. Some entries are hard to read and are marked [?].]
Left column
What I Know
[transcriber’s note: the answer numbers and letters for this section are printed in two columns and are hard to read in the rotated image. Readable entries follow.]
- D A 6.
- B A 7.
- D A 8.
- B C 9.
- C C 10.
What is It
Activity 1: What’s My Name
- Pt. O
- BO, DO, AO, CO
- AB, CD
- CD, AB, AD, BD, BC, AC
- DCB, ACD, BDA, CBD, ACB, CDA, ACB, ABD
Activity 2: Name Me
- PY, OP, PR, NP, PT, PS
- RN, ST
- NT, OT, ST, RN
- RPO, OPN, NPY, RPY, etc.
- RX
- OT
- STN, RNT, OTN, OTS, etc.
Activity 3: Identify Me
- radius
- tangent line
- point of tangency
- center
- inscribed angle
- central angle [?]
- chords
Activity 4: Match – Up
- F
- C
- D
- E
- G
- H
- B
Right column
What I Have Learned
Activity 5: Identify Me
- circle
- chord
- diameter
- radius
- central angle
Activity 6: Hunt Me
[illustration: word-search grid with the ten words circled in the answer key]
Assessment
- B
- B
- D
- B
- D
- C
- B
- A
- C
- C
Additional Activities
a. Pt. B b. BC, BM, BP, BO c. OM d. ∠CBO, ∠OBP, ∠CBP, ∠CBM, ∠MBP e. DN, OQ, OM f. CD, DO, OC, OP, PQ, QM, NM, QN, PN g. OPN, COQ, DPQ, OPC, PMD, PMO
References
Lumbre, Angelina P., Ursua, Alvin. C., Placer, Donnel P., Burgos, Jaime R. (2016). Circle and Its Parts. 21st Century Matheletes. Vibal Group Inc. pp. 232-235.
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
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