Mathematics 5 Quarter 3 Module 7: Regular and Irregular Polygons

Mathematics Quarter 3 – Module 7: Describing and Comparing Properties of Regular and Irregular Polygons

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Mathematics

Quarter 3 – Module 7: Describing and Comparing Properties of Regular and Irregular Polygons

CO_Q3_Mathematics 5_ Module 7

Mathematics – Grade 5 Alternative Delivery Mode Quarter 3 – Module 7: Describing and Comparing Properties of Regular and Irregular Polygons First Edition, 2020

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Writers: Egie B. Tamoyang Editors: Niann L. Atis, Carlito Labine Reviewers: Renato S. Cagomoc, Rolando M. Lacbo, Joshua Sherwin T. Lim, Pedro Montecillo 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

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Mathematics

Quarter 3 – Module 7: Describing and Comparing Properties of Regular and Irregular Polygons

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

Good day, Mathlete! In this module, you are going to learn about polygons by describing its parts and comparing the properties of regular and irregular polygons. Knowing these makes you appreciate the importance of polygons in our day-to-day living.

After going through this module, you are expected to:

• Describe and compare properties of regular and irregular polygons.

But first, let us check what you have learned so far about polygons.

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CO_Q3_Mathematics 5_ Module 7

What I Know

Directions: Read and understand the questions that follow. Choose the letter that corresponds to the correct answer. Write your answer on a separate sheet of paper.

1. Which of the following is NOT a polygon?
   a. [illustration: trapezoid-like closed figure with straight sides]
   c. [illustration: arrow-shaped figure with straight sides]
   b. [illustration: closed figure with one curved side]
   d. [illustration: irregular closed figure with straight sides]

   
   

2. Which of the following is TRUE about a regular polygon?
   I. The lengths of the sides of a regular polygon are equal.
   II. The measures of the interior angles are equal.
   a. I only
   c. I and II
   b. II only
   d. Neither I nor II

   
   

For items 3 and 4, identify the given polygon and tell whether it is regular or irregular.

3. [illustration: arrow-shaped polygon with straight sides]
   a. heptagon – irregular
   c. heptagon – regular
   b. hexagon – irregular
   d. hexagon – regular

   
   

4. [illustration: octagon-shaped figure with a circle inside and radial lines]
   a. pentagon – irregular
   c. heptagon – regular
   b. octagon – regular
   d. decagon – irregular

   
   

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CO_Q3_Mathematics 5_ Module 7

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CO_Q3_Mathematics 5_ Module 7

5. Which of the following is an instrument used to draw a circle? Which of the following is NOT a regular polygon?
   a. [illustration: regular hexagon]
   b. [illustration: regular pentagon]
   c. [illustration: triangle]
   d. [illustration: rectangle]

   
   

   [transcriber’s note: the choices shown are polygon figures, not instruments; the item is printed as shown]

   
   

6. Which is a 4-sided regular polygon?
   a. Trapezoid
   b. Rectangle
   c. Parallelogram
   d. Square

   
   

For item no. 7, please refer to the situation below.

Rolly measured the angles of a pentagon. The table below shows the measures of the internal angles of the pentagon.

Angles	Measure
∠A	90°
∠B	110°
∠C	110°
∠D	150°
∠E	80°

7. What can be concluded about the pentagon?
   a. It is a regular polygon because it has a pair of congruent angles.
   b. It is a regular polygon because not all angles measure more than 75°[?].
   c. It is an irregular polygon because not all angles have the same measure.
   d. It is an irregular polygon because there are only two angles with equal measures.

   
   

8. A regular octagon has a perimeter of 40 cm. How long is its side?
   a. 5 cm
   b. 8 cm
   c. 10 cm
   d. 20 cm

   
   

For item no. 9 and 10, please consider the given below.

Given: ABCDEF is a regular polygon The measure of AB is 2 cm The measure of ∠C = 120°

[illustration: regular hexagon labeled A, B, C, D, E, F with equal side marks]

9. Which could be the measure of line segment DE?
   a. 2 cm
   b. 4 cm
   c. 6 cm
   d. 12 cm

   
   

10. What is the possible measure of ∠E?
    a. 54°
    b. 100°
    c. 108°
    d. 120°

    
    

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CO_Q3_Mathematics 5_ Module 7

Lesson 1: Describing and Comparing Properties of Regular and Irregular Polygons

To fully understand this lesson, you should have already learned about visualizing, naming, and describing polygons. Understanding shapes is important in mathematics, but it also has many practical applications in real-life situations. Professionals such as engineers, architects, artists, real-estate agents, farmers and construction workers deal with shapes in their workplace.

So, are you ready to learn? Let’s begin.

What’s In

Before we describe and compare the properties of regular and irregular polygons, let us review how to visualize, name and describe polygons with 5 or more sides.

You learned in the previous lesson that a polygon is a closed plane figure that is formed by the line segments that meet only at their endpoints. The line segments are the sides and the endpoints where sides meet are the vertices. The two adjacent sides form an angle. Plane figures like circles or any other shape that includes a curve are not considered polygons.

Figures 1 and 2 below are examples of polygon.

[illustration: Figure 1, a pentagon with vertices A–E and angles marked, and Figure 2, an irregular open-looking polygon with vertices A–G and angles marked; labels “Sides,” “Angle,” and “Vertex” with arrows pointing to parts of the figures]

Figure 1

Figure 2

Figure 1 has five sides, five angles and five vertices. Its sides are (AB), (BC), (CD), (DE), (EA). Its angles are ∠A, ∠B, ∠C, ∠D, ∠E. Its vertices are A, B, C, D and E.

Can you name the sides, angles and vertices of figures 2?

The figures below are non-polygons. Can you tell why?

[illustration: five non-polygon figures: a bow-tie shape made of two triangles meeting at a point, an ellipse, a rounded rectangle, a shape with one curved side, and an L-shaped figure]

Polygons are identified according to the number of sides that they have. Here are the different polygons and their identification.

Polygons	Identification	Number of Sides
[illustration: triangle outline]	triangle	3
[illustration: parallelogram outline]	quadrilateral	4
[illustration: pentagon outline]	pentagon	5
[illustration: hexagon outline]	hexagon	6
[illustration: arrow shape with a point on the right]	heptagon	7
[illustration: octagon outline]	octagon	8
[illustration: nonagon outline]	nonagon	9
[illustration: decagon outline]	decagon	10
[illustration: undecagon outline]	undecagon	11
[illustration: six-pointed star outline]	dodecagon	12

Now, answer the exercise below and let’s see how much you remember about the lesson from the previous module.

Example 1:

The objects listed below are all around us. Identify each polygon.

1. [illustration: pentagon-shaped pedestrian crossing sign with two walking figures]

   
   

2. [photo: hexagon-shaped glass jar with a lid, filled with balls]

   
   

3. [illustration: concentric polygon outlines, one inside another]

   
   

4. [illustration: octagon-shaped wall clock with the numbers 1 to 12]

   
   

5. [illustration: polygon with many vertices connected by interior lines]

   
   

What’s New

Polygons are all around us. A lot of polygons can be found in our homes and in the community where we live in.

For example, when you travel on streets, you see road signs. Most of these have the shape of a polygon. A polygon is any shape made up of line segments that can be drawn on a flat surface, like a piece of paper. Such shapes include squares, rectangles, triangles and pentagons.

The following figures are examples of polygons around us. Can you determine what these are and where you typically see them?

[illustration: row of five road signs: a pentagon-shaped pedestrian crossing sign, an octagonal sign labeled “STOP”, a triangular sign with two lanes narrowing, a circular no-parking sign with an arrow, and a diamond-shaped right-turn sign]

[illustration: row of five polygon examples: a honeycomb pattern, a hexagonal glass jar filled with balls, an octagonal wall clock, concentric polygon outlines, and an octagonal manhole cover]

What Is It

In the previous module, you were taught on how to visualize, name and describe polygons with 5 or more sides. This new lesson is going to teach you how to describe and compare properties of polygons that will help you classify them as either regular or irregular.

The pictures above show samples of regular and irregular polygons. Which of these are regular and which are irregular? For you to determine regular and irregular polygons, you need to look at the sides and angles.

When working with polygons the properties are the number of sides of the shape, the angles in the shape, and the length of the sides of the shape.

The following are examples of regular polygons:

[illustration: four regular polygons in a row: a triangle, a square, a regular pentagon, and a regular hexagon]

The following are examples of irregular polygons:

[illustration: eight irregular polygons in two rows of four]

Activity 1:

Materials: Ruler, protractor, pencil, paper

Procedure:

1. Using your ruler, measure the sides of the polygons given above. Write the measure of each side.
2. Using your protractor, measure the internal angles of the given polygons. Write the measure of each of the internal angles.

What did you find out?

A polygon which has all its sides of equal length and all its angles of equal measures is called a regular polygon.

Here are the different shapes in regular forms:

[illustration: regular pentagon, regular hexagon and regular octagon, with tick marks on the sides showing equal length]

Regular pentagon Regular hexagon Regular octagon

The marks on the sides of the polygons indicate equal length.

A polygon that is NOT a regular polygon is called an irregular polygon.

Here are the different shapes in irregular forms:

[illustration: irregular pentagon, irregular hexagon and irregular octagon, with tick marks on some sides]

Irregular pentagon Irregular hexagon Irregular octagon

Example:

1. [illustration: triangle ABC with vertices labeled A (top), B (bottom left) and C (bottom right); tick marks on all three sides and arcs at all three angles]

All sides of this triangle are in equal length, all angles are equal. Therefore, it is a regular polygon.

2. [illustration: quadrilateral ABCD, a rectangle-like figure with vertices labeled A (top left), B (top right), C (bottom left) and D (bottom right); right-angle marks at the corners and tick marks on opposite sides]

In the adjoining figure of a quadrilateral there are four sides, where the opposite sides are equal such as, AB = CD and AC = BD. AB is not equal to BD. Therefore, this is an irregular polygon.

3. [illustration: quadrilateral ABCD, a trapezoid with vertices labeled A (top left), B (top right), C (bottom left) and D (bottom right); arcs marking angles A and B, and angles C and D]

The measure of ∠A is equal to the measure of ∠B. The measure of ∠C is equal to the measure of ∠D, but not all four angles are congruent. Therefore, this is an irregular polygon.

4. [illustration: regular octagon with vertices labeled A through H, tick marks on all eight sides]

All eight sides of this polygon are equal in length. Similarly, all of its angles are equal. Therefore, this octagon is a regular polygon.

5. [illustration: rhombus ABCD with vertices labeled A (bottom left), B (top left), C (top right) and D (bottom right); arcs marking the angles]

All four sides are the same length, like a square that has been squashed sideways, but not all four angles are congruent. Therefore, this rhombus is an irregular polygon.

What’s More

Activity 1 Know Me Well!

Directions: Identify the kind of polygon being described. Choose your answer from the box.

1. I am a 3-sided polygon with congruent sides.
2. I have one pair of parallel sides.
3. I am a six-sided polygon. All my sides are congruent.
4. I am a 3-sided polygon with 2 congruent sides
5. My 4 sides are equal. All my sides form right angles.

[transcriber’s note: the word box is printed in three columns, read row by row]

equilateral triangle · rhombus · trapezoid isosceles triangle · square · Regular Hexagon

Activity 2 Fill My Table!

Directions: Read For each figure, count the number of sides, name the polygon and identify if it is regular or irregular.

Figure	Number of Sides	Name of Polygon	Regular or irregular?
1) [illustration: triangle outline]
2) [illustration: square with one cut corner]
3) [illustration: octagon outline]
4.) [illustration: irregular hexagon, shaded]
5) [illustration: octagon outline]

Activity 3 Pick a Tick!

Directions: Name each polygon by the number of its sides. Tell whether it is regular or irregular.

1. [illustration: chevron-shaped polygon]
2. [illustration: polygon with many sides, shaded]
3. [illustration: irregular polygon with a notch on the right side]
   .4) [illustration: regular pentagon]
4. [illustration: arrow-shaped polygon]

What I Have Learned

Directions: Fill in the blank with the correct word to make the statement true.

1. _____ are closed plane figures that are formed by straight line segments that meet only at their endpoints.
2. _____ are the sides of a polygon.
3. Polygons are classified according to the number of its _____.
4. _____ are quadrilaterals with 1 pair parallel sides.
5. _____ are polygons with all of its sides and angles equal.
6. _____ are quadrilaterals with 4 right angles & have all sides equal.
7. _____ is a five-sided polygon with equal sides and equal angles.
8. _____ are polygons that have non-congruent sides.
9. _____ is an eight-sided polygon with unequal sides.
10. _____ is a three-sided polygon with equal sides.

Excellent job! Let’s try some more activities to strengthen what you have learned.

What I Can Do

Directions: On a sheet of bond paper, draw at least 5 regular polygons. Color the polygons and make it your work of art. Be creative!

Let’s check what you have learned. Answer the activity below.

Assessment

A. Directions: Read and understand the questions that follow. Choose the letter that corresponds to the correct answer. Write your answer on a separate sheet of paper.

1. Which of the following is a polygon?
   a. [illustration: oval outline]
   b. [illustration: shape with curved sides]
   c. [illustration: rectangle with rounded corners]
   d. [illustration: irregular shape with straight sides and a notch]

   
   

2. Which of the following statements is TRUE about an irregular polygon?
   I. The lengths of the sides of an irregular polygon are not equal.
   II. The measures of all the interiors angles are equal.
   a. Statements I only
   b. Statements II only
   c. Both Statements I and II
   d. Neither I nor II

   
   

For items 3 and 4, identify the given polygon and tell whether it is regular or irregular

3. [illustration: five-pointed star]
   a. octagon – irregular
   b. octagon – regular
   c. decagon – irregular
   d. decagon – regular

   
   

4. [illustration: concentric polygons nested inside one another]
   a. octagon – regular
   b. heptagon – regular
   c. pentagon – irregular
   d. decagon – irregular

   
   

5. Which of the following is a REGULAR POLYGON?
   a. [illustration: hexagon]
   b. [illustration: pentagon]
   c. [illustration: triangle]
   d. [illustration: square]

   
   

6. Which is a 3- sided regular polygon?
   a. scalene triangle
   b. isosceles triangle
   c. equilateral triangle
   d. obtuse triangle

   
   

For items 7 and 8, please consider the given below.

Given: PLANE is a regular polygon. The measure of 𝑃𝐿̅̅̅̅ is 4 cm The measure of ∠N = 108°

[illustration: regular pentagon with vertices labeled P, L, A, N, E and tick marks on its sides]

7. Which could be the measure of line segment PE?
   a. 2 cm
   b. 4 cm
   c. 6 cm
   d. 12 cm

   
   

8. What is the possible measure of ∠L?
   a. 54°
   b. 100°
   c. 108°
   d. 120°

   
   

For item 9, please refer to the situation below.

Eric measured the angles of a hexagon. The table at the right shows the measures of the internal angles of the hexagon. He also measured the sides of the hexagon and found them to be equal.

Angles	Measure
∠A	120°
∠B	120°
∠C	120°
∠D	120°
∠E	120°
∠F	120°

9. What can be concluded about the hexagon?
   a. It is a regular polygon because all angles are equal and all sides are equal.
   b. It is a regular polygon because it has a pair of congruent angles.
   c. It is an irregular polygon because all angles measure 120°.
   d. It is an irregular polygon because all angles measure less than 180°.

   
   

10. A regular hexagon has a perimeter of 42cm. How long is its side?
    a. 6 cm
    b. 7 cm
    c. 14 cm
    d. 21 cm

    
    

Congratulations! Just one more activity and you are done with this module.

Good luck!

Additional Activities

Directions: Name each polygon inside the grid paper. Tell whether it is a regular or an irregular polygon.

[illustration: grid paper with five gray polygons, labeled 1 to 5 as printed on the shapes]

Answer Key

transcriber’s note: this page is printed with its boxes upside down. The answers below are read from the rotated print, and the What I Know answers in particular are uncertain.

What I Know

1. [?] B
2. [?] C
3. [?] A
4. [?] B
5. [?] D
6. [?] D
7. [?] C
8. [?] A
9. [?] A
10. [?] D

What’s In

6. Pentagon
7. Hexagon
8. Heptagon
9. Octagon
10. Undecagon

What’s More

Activity 1:

1. Equilateral Triangle
2. Trapezoid
3. Regular Hexagon
4. Isosceles triangle
5. Square

Activity 2:

1. regular – triangle – 3 sides
2. irregular – pentagon – 5 sides
3. regular – dodecagon – 12 sides
4. irregular – hexagon – 6 sides
5. regular – heptagon – 7 sides

Activity 3:

1. Irregular hexagon
2. Regular dodecagon
3. Irregular octagon
4. Regular pentagon
5. Irregular octagon

What I Have Learned

1. Polygons
2. Line Segments
3. Sides
4. Trapezoids
5. Regular Polygons
6. Squares
7. Regular Pentagon
8. Irregular Polygons
9. Irregular Octagons
10. Equilateral Triangle

What I Can Do

Answers vary but the polygons must be regular polygon

Assessment

1. D
2. A
3. C
4. B
5. D
6. C
7. B
8. C
9. A
10. B

Additional Activities

1. Octagon – Irregular
2. Octagon – Irregular
3. Heptagon – Irregular
4. Hexagon – Irregular
5. Decagon – Irregular

References

K to 12 Grade 5 Curriculum Guide, p 61, Lesson Guide in Elementary Mathematics 5, p. 354-357

2011-2021, (., n.d. Properties of Polygons | Skills You Need. [online] Skillsyouneed.com. Available at: <https://www.skillsyouneed.com/num/polygons.html> [Accessed 4 March 2021].

The School Run. n.d. What are regular and irregular shapes? [online] Available at: <https://www.theschoolrun.com/what-are-regular-and-irregular-shapes> [Accessed 4 March 2021].

Math Only Math. n.d. Regular and Irregular Polygon | Examples of Irregular and Regular Polygon. [online] Available at: <https://www.math-onlymath.com/regular-and-irregular-polygon.html> [Accessed 4 March 2021].

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