DEPARTMENT OF EDUCATION DIVISION OF SAN JOSE DEL MONTE CITY San Ignacio St., Poblacion, City of San Jose del Monte, Bulacan 3023
Mathematics Quarter III – Module 5 Polygons
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Mathematics - Grade 7 Alternative Delivery Mode Quarter 3 - Module 5: Polygons
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7 Mathematics Quarter III – Module 5 Polygons
Department of Education • Republic of the Philippines
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. 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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What I Need to Know
CONTENT STANDARD The learner will be able to demonstrates understanding of key concepts of geometry of shapes and sizes, and geometric relationships.
PERFORMANCE STANDARD The learners will be able to create models of plane figures and formulate and solve accurately authentic problems involving sides and angles of a polygon.
LEARNING COMPETENCY The learner illustrates polygons: (a) convexity; (b) angles; and (c) sides. Learning Objectives At the end of the lesson, you are expected to: 1. Define and illustrate polygons; 2. Determine polygons and non – polygons; 3. Identify a convex and non – convex polygons; and 4. Solve for the measure of sides of polygon.
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What I Know Direction: Write the letter of the correct answer on a separate sheet of paper. 1. Which of the following polygons has 11 sides? A. decagon B. dodecagon C. nonagon
D. undecagon
2. How many vertices are there in a pentagon? A. 5 B. 6 C. 7
D. 8
3. Which of the given figure is a convex polygon? A.
B.
C.
4. Which of the following figures is a polygon? A. B. C.
D.
D.
5. How many angles are there in a regular quadrilateral? A. 4 B. 5 C. 6 D. 7 6. In quadrilateral ABCD, which are considered as consecutive vertices? A. A and B B and C C and D A and D
C. AB, BC, CD, AD
B. A, B, C and D
D. ∠A, ∠B, ∠C, ∠D
7. Which of polygon has 6 sides? A. decagon B. heptagon
C. hexagon
D. triangle
8. In polygon ABCDE, how many possible diagonals can be formed from one vertex? A. 5 B. 4 C. 3 D. 2 9. What is the term that refers to a closed plane figure determined by the union of non – collinear? A. angle B. line C. plane D. polygon
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10. A polygon where all angles and sides are congruent is ________. A. consecutive B. equiangular C. equilateral D. regular 11. Which is a non-convex polygon? A. B. C.
D.
For item numbers 12 – 15, refer to regular pentagon STAND. N D
A
S
T
12. Another name for regular pentagon STAND is _________. A. STDAN B. ANDST C. DTSNA D. ANSTD 13. If the perimeter of the regular pentagon STAND is 115, what is the measure of TA? A. 23 B. 27 C. 55 D. 115 14. In regular pentagon STAND, ∠𝐴 and ∠𝐷 are considered _______. A. consecutive vertices C. non – consecutive angles B. non - consecutive sides D. consecutive angles 15. Which of the following is a pair of consecutive sides of regular pentagon STAND? A. NA and AT B. TA and DS C. ST and NA D. DS and NA
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What’s In
A. Given the figure below, choose from the words inside the box that best describes each item. A D
⍳1
I
F JJ K
B C ⍳2
M
L
E
P N O
H F G
⍳4
⍳3 Interior Angle Exterior Angle Parallel
Corresponding Angle Alternate Interior Angle Alternate Exterior Angle
_________1. ∠C, ∠P, ∠J, ∠E _________2. ∠A and ∠O _________3. ∠B and ∠P _________4. ∠L, ∠G, ∠N, ∠A _________5. ∠K and ∠G B. Using the figure in item A, if m∠J = 95˚, find the measure of the following: 1. m∠G = _______________ 2. m∠A + m∠D = _________ 3. m∠P = _______________ 4. m∠H = ______________ 5. m∠N − m∠O = ________
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What’s New
Activity: Who Am I? Direction: Complete the table by naming the polygon. Figure
Number of Sides
Name of the Polygon
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What is It Activity: Word Pool. Direction: Choose from the box below the correct word that describes each sentence. Write your answer on a separate sheet of paper. Equiangular
Convex
Polygon
Equilateral
Regular
Vertex
1. It is a point where two or more lines or segments meet to form an angle. 2. A polygon where all its interior angles are less than 180 ˚. 3. It refers to a triangle where all sides are congruent. 4. A closed plane figure where it is determined by non – collinear segments that meets on a common endpoint. 5. All angles of a triangle are congruent.
What is a polygon? How do you describe it?
A polygon comes from two Greek words “poly” which means “many” and “gon” which means “angles”. It is a closed plane figure that is determined by its non – collinear segments (sides) that meets on a common endpoint. (vertex).
A polygon can be described by its angles, number of its sides, and whether any of its sides are congruent. We can classify and name polygons according to the number of their sides. For example: Number of Sides (n) 3 4 5 6 7 8 9 10 11 n
Name of the Polygon Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Undecagon/Hendecagon n - gon
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Look at the given example, polygon JADE. J
E
A
D
We can name this polygon according to the order of the consecutive vertices (vertices that are on the same side of the polygon) such as JADE or JEDA or ADEJ or DEJA.
Also, polygon JADE is composed of four sides these are non – collinear segments, JA, AD, DE and EJ and four angles, namely, ∠J, ∠A, ∠D and ∠E. Thus, specifically, we can say that polygon JADE is a 4-gon or a quadrilateral. Moreover, as you notice, segments JA, AD, DE and EJ are of the same length, or have congruent sides and the angles are perpendicular - meaning that the angles are equal to 90˚. Therefore, this kind of a polygon and type of a quadrilateral is a square. Since, a square has four congruent sides and four congruent angles, we can describe this kind of polygon as a regular polygon. A regular polygon is a type of polygon that is both equilateral (all sides are congruent) and equiangular (all angles are congruent).
Some examples of regular polygons are as follow,
There are figures that cannot be considered as polygons. These are called non – polygons because they do not have the properties or do not satisfy the criteria of polygons. For instance,
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Convex and Non – Convex Polygon A polygon is convex if and only if a line containing its side or its extended side does not cross the interior of the polygon. A polygon that is not convex is called non – convex.
Examples of convex polygons,
Given an example hexagon MONITA, extending its sides such as shown below, M
O N
A
T
there are no two points lie on opposite sides of a line containing a side of the polygon.
I
Examples of non – convex polygons,
If we extend the sides of any non – convex polygon, there are points that lie inside it as shown below.
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What’s More Activity 1: What Am I? A. Determine if the given figure is a polygon or not. Write P if it is a polygon and NP if it is not.
_______ 1.
_______ 2.
_______ 3.
_______ 4.
_______ 5.
B. Identify whether the polygon is convex polygon or not. Write C if it is convex polygon and NC if it is not convex.
______ 1.
______ 2.
.
______ 3.
______ 4.
______ 5.
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Activity 2: Find Me! Given a regular octagon, ABCDEFGH, answer the following:
A
1. Line DE and EF - _________________
B
2. Angles C and D - _________________ H
G
F
E
C
3. Angles A and E - _________________
D
4. How many diagonal lines can be drawn from one vertex of the given polygon? _________________________________ 5. If the measure of segment DE is 24.5 cm, what is the measure of segment HG? _________________________________
What I Have Learned
Direction: Inside each hexagon, write down facts you have learned from the lesson.
____________ ____________ ____________
I learned that _______________ _______________ _______________ _______________ _______________
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What I Can Do
Activity: Art Within Me! Direction: Create a tessellation using at least 2 regular polygons. Your tessellation (pattern) should cover the entire paper. Materials: Ruler, Pen or Pencil, Coloring Materials, Bond Paper Rubrics: Criteria Complexity of Design Originality Precision Use of Color Neatness Total
Possible Points 40 30 10 10 10 100
Sample of Tessellation:
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Points Earned
Assessment
Direction: Write the letter of the correct answer on a separate sheet of paper. 1. Which is considered a four – sided polygon? A. octagon B. pentagon C. rhombus
D. triangle
2. How many vertices are there in a hendecagon? A. 10 B. 11 C. 12
D. 13
3. Which of the figures is a non - convex polygon? A. B. C.
D.
4. Which of the following figures is a polygon? A. B. C.
D.
5. If a side of a regular decagon is 10 meters, what is the measure of its perimeter? A. 1800 B. 1400 C. 1000 D. 800 6. Which is a non – consecutive side of a pentagon SMILE? A. SM and IL B. SM and IM C. MI and IL D. IL and EL 7. Which of the polygon has 9 vertices? A. decagon B. heptagon C. hexagon
D. nonagon
8. In polygon ABCD, how many diagonals can be formed? A. 0 B. 1 C. 2
D. 3
9. In triangle MAN, all sides are equal. If MA = 16cm, what is the measure of MN? A. 8 B. 16 C. 32 D. 64 10. In a quadrilateral BEST, BE is congruent to ST. If BE = 5cm, what is the measure of ST? A. 5 B. 10 C. 20 D. 25 11. Which figure is considered a regular polygon? A. B. C.
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D.
12. Which is the consecutive vertices of pentagon CHONA? A. C,O,N,H,A B. C,H,A,N,O C. H,O,N,C,A D. A,N,O,H,C 13. How many interior angles are there in a regular 36 – gon? A. 36 B. 24 C. 12 D. 10 14. If one of the sides of a 32 – gon is 45 cm, what is the perimeter of the polygon? A. 540 B. 1440 C. 2880 D. 5760 15. Which of the following figures is a convex? A. B. C.
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D.
Additional Activities Direction: Draw diagonal lines for each given polygon. Complete the table by finding the diagonals of the polygon. Polygon Example:
Number of Diagonals from One Vertex 1
1.
2.
3.
4.
5.
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Total Number of Diagonals 2
What I Know 1. D 2. A 3. B 4. B 5. A 6. A 7. C 8. D 9. D 10. D 11. B 12. B 13. A 14. C 15. A
What’s More Activity 2: 1. Consecutive Sides 2. Consecutive Angles 3. Non-consecutive angles 4. 5 5. 24.5 cm.
What’s In A. 1. Interior Angles 2. Alternate Exterior Angles 3. Alternate Interior Angles 4. Exterior Angles 5.Corresponding Angles B. 1. 85˚ 2. 180˚ 3. 95˚ 4. 95˚ 5. 10˚
15 What’s New 1. triangle 2. quadrilateral 3. pentagon 4. hexagon 5. heptagon 6. octagon 7. nonagon 8. decagon 9. undecagon 10. dodecagon What Is It
What’s More Activity 1 A. 1. P 2. NP 3. P 4. NP 5. P B. 1. C 2.NC 3. NC 4. C 5. NC
1. vertex 2. convex 3. equilateral 4. polygon 5. equiangular
What I Have Learned
Assessment 1. C 2. B 3. A 4. B 5. C 6. A 7. D 8. C 9. B 10. A 11. B 12. D 13. A 14. B 15. A
What I Can Do
Additional Activities 1. 3; 9 2. 1; 2 3. 2; 10 4. 5; 20 5. 0; 0
Answer Key
References Bautista, Evangeline P., Cabral, Emmanuel A., Garces, Ian June L., Sarmiento, Jumela F., de Lara- Tuprio, Elvira P, Marasigan, Jose A., Experiencing Mathematics (Math XP) Series Geometry III, Vibal Publishing House, Inc., 2008 Department of Education, Mathematics 7, Learner’s Material, First Edition, 2013 Department of Education, Mathematics 7, Teacher’s Guide, First Edition, 2013 Romero, Karl Freidrich Jose D., Geometry in the Real World Explorations and Applications, Salesiana Publishers, Inc., 2003
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This material was contextualized and localized by the Learning Resource Management and Development Section (LRMDS)
SCHOOLS DIVISION OF SAN JOSE DEL MONTE Officer-in-Charge Office of the Schools Division Superintendent ERICSON S. SABACAN EdD, CESO VI Assistant Schools Division Superintendent ROLANDO T. SOTELO DEM Chief Education Supervisor Curriculum Implementation Division ANNALYN L. GERMAN EdD Education Program Supervisor, LRMS MA. CORAZON P. LOJA Education Program Supervisor, Mathematics MARIAN A. HEBULAN Muzon Harmony Hills High School Writer MARIAN A. HEBULAN Muzon Harmony Hills High School Illustrator MARIAN A. HEBULAN Muzon Harmony Hills High School Layout Artist BERNADETTE F. ANCHETA Sapang Palay National high School Content Editor DONN URIEL D. BUENAVENTURA Kaypian National High School Language Reviewer MICHAEL B. ZAMORA Sapang Palay National High School Lay-out Evaluator
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For inquiries or feedback, please write or call: Department of Education – Division of San Jose Del Monte City – Learning Resource Management and Development Section (LRMDS) San Ignacio Street, Poblacion, City of San Jose Del Monte, Bulacan Email Address: [emailprotected]
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