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Mathematics 7 Unit 1: Angles and Polygons Lesson 1 Constructing Regular and Irregular Polygons Table of Contents Introduction 1 Learning Competencies...

Mathematics 7 Unit 1: Angles and Polygons Lesson 1 Constructing Regular and Irregular Polygons Table of Contents Introduction 1 Learning Competencies 2 Learning Targets 2 Warm-Up 2 Learn about It 4 Polygons 4 Regular and Irregular Polygons 5 Constructing Regular Polygons 7 Let’s Practice 9 Check Your Understanding 14 Key Points 16 Self-Assessment 16 Reflection 17 Attributions 18 References 18 Answer Key 19 0 Mathematics 7 Unit 1: Angles and Polygons 1 Constructing Regular and Irregular Polygons A tangram is a puzzle using polygons to create new shapes. Introduction Polygons are all around us! From the design of a soccer ball to the structure of houses, these geometric figures play a role in our daily lives. This lesson will delve into understanding the difference between regular and irregular polygons and how to construct them using simple tools like a ruler and a protractor. Let us jump into this interesting world of shapes and angles! 1.1. Constructing Regular and Irregular Polygons 1 Mathematics 7 Unit 1: Angles and Polygons Learning Competencies At the end of this lesson, the learners should be able to do the following: Draw and describe regular and irregular polygons with 5, 6, 8, or 10 sides based on measurements of sides and angles using a ruler and protractor. Draw triangles, quadrilaterals, and regular polygons (5, 6, 8, or 10 sides) with given angle measures. Learning Targets In this lesson, you should be able to do the following: Define regular and irregular polygons and determine the characteristics of polygons with 5, 6, 8, or 10 sides. Utilize a ruler and protractor to measure sides and angles accurately for constructing regular and irregular polygons. Draw and describe triangles, quadrilaterals, and regular polygons (5, 6, 8, or 10 sides) with given angle measures. Warm-Up Name That Polygon! 21st Century Skills Icons Legend Information, Media, and Technology Skills Communication Skills Learning and Innovation Skills Life and Career Skills 1.1. Constructing Regular and Irregular Polygons 2 Mathematics 7 Unit 1: Angles and Polygons Procedure 1. Draw a five-sided shape on a piece of paper. 2. Try to make all sides and angles equal. 3. Label the number of sides and angles you used. Guide Questions 1. What did you name your five-sided shape? _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ 2. Were you able to make all sides and angles equal? What challenges did you encounter? _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ Essential Question(s) What makes a polygon regular? How do you draw a regular polygon using a ruler and a protractor? 1.1. Constructing Regular and Irregular Polygons 3 Mathematics 7 Unit 1: Angles and Polygons Learn about It Polygons In the Warm-Up activity, you created a five-sided shape. Was it difficult to make the sides and angles have equal measures? This five-sided shape is called a polygon. If a polygon has sides and angles that have equal measures, then we call it a regular polygon. De nition of Terms A polygon is a closed figure made up of polygon line segments. Did You Know? The word polygon comes from the Greek words poly meaning "many" and gonia meaning "angle." A polygon essentially means "many angles." The following are examples of polygons. Note that polygons have vertices, angles, and sides. Figure 1. Examples of polygons and their parts 1.1. Constructing Regular and Irregular Polygons 4 Mathematics 7 Unit 1: Angles and Polygons Take note of the following parts of a polygon: The side refers to the line segments that enclose the polygon. The vertex (plural: vertices) refers to the point of intersection of the sides of a polygon. The angle refers to the opening that the two sides form. Regular and Irregular Polygons Regular polygons are polygons that have all sides of equal length and all angles of equal measure. Examples include equilateral triangles, squares, and regular hexagons. Polygons that do not have sides of equal length or angles of equal measure are called irregular polygons. De nition of Terms Regular polygons are polygons that have regular polygons all sides of equal length and all angles of equal measure. The following are examples of regular and irregular polygons. 1.1. Constructing Regular and Irregular Polygons 5 Mathematics 7 Unit 1: Angles and Polygons The different types of regular polygons are as follows. Regular Polygon Number of Sides Figure equilateral triangle 3 square 4 regular pentagon 5 regular hexagon 6 regular octagon 8 regular decagon 10 1.1. Constructing Regular and Irregular Polygons 6 Mathematics 7 Unit 1: Angles and Polygons Tip Note that in this lesson, we will only be covering triangles, squares, pentagons, hexagons, octagons, and decagons. A more in-depth discussion of the different types of polygons will be covered in Lesson 3: Types of Polygons. Constructing Regular Polygons Regular polygons can be constructed using a ruler and a protractor. Let us try constructing a square using a ruler and a protractor. Step 1: Draw a line. It could be of any length. Let us say that the length of the square is 5 cm. Step 2: At one end of the line, measure and draw another line at that angle. Make sure that the new line measures 5 cm. 1.1. Constructing Regular and Irregular Polygons 7 Mathematics 7 Unit 1: Angles and Polygons Tip In constructing regular polygons, you have to know the measure of its interior angles by using a ruler and a protractor. The angles of a regular triangle measure. The angles of a square measure. The angles of a regular pentagon measure. The angles of a regular hexagon measure. The angles of a regular octagon measure. The angles of a regular decagon measure. Note that there is a formula for solving the interior angles of a polygon, but this will be discussed in detail in Lesson 4: Interior and Exterior Angles of a Convex Polygon. Step 3: Do the same for the other end of the line and connect the remaining endpoints to form the last side. 1.1. Constructing Regular and Irregular Polygons 8 Mathematics 7 Unit 1: Angles and Polygons Practical Applications The concept of regular and irregular polygons can be found in different disciplines. Science: The structure of crystals can resemble certain regular polygons. Art and Design: Polygons are used in various designs and patterns to create visually appealing structures. Architecture: Polygons, especially triangles and quadrilaterals, form the basis of structural designs for many buildings. Let’s Practice Example 1 Determine if the following figure is a regular polygon or not. 1.1. Constructing Regular and Irregular Polygons 9 Mathematics 7 Unit 1: Angles and Polygons Solution Step 1: Check the sides of the polygon. Notice that one of the sides measures 3 cm. The other sides also measure 3 cm based on their tick marks. Thus, all of the sides have equal measures. Step 2: Check the angles of the polygon. Notice that one of the angles measures. The other angles also measure based on their tick marks. Thus, all of the angles have equal measures. Since all of the sides and angles have equal measures, it follows that this figure is a regular polygon. Let’s Try It Determine if the following figure is a regular polygon or not. Example 2 Construct a regular pentagon. Solution A regular pentagon has 5 sides. Each angle measures. 1.1. Constructing Regular and Irregular Polygons 10 Mathematics 7 Unit 1: Angles and Polygons Step 1: Draw a line of any length. Let us use 3 cm as our length. Step 2: At one end of the line, use a protractor to measure and draw the next line at that angle. Make sure that the next line also measures 3 cm. Step 3: Repeat Step 2 until you complete the pentagon. Let’s Try It Construct a regular hexagon. 1.1. Constructing Regular and Irregular Polygons 11 Mathematics 7 Unit 1: Angles and Polygons Example 3 Construct a triangle with angles measuring , , and. Solution Step 1: Draw a side of any length. Step 2: Using a protractor, construct the angle of at one end of the side. Step 3: At the other end of the side, construct a angle. Step 4: Connect the two lines to form the triangle. The final angle should have a measure of. Let’s Try It Construct a quadrilateral with angles measuring , , , and. 1.1. Constructing Regular and Irregular Polygons 12 Mathematics 7 Unit 1: Angles and Polygons Real-World Problems Example 4 John is trying to fence a garden in the shape of a regular octagon. His fencing materials can reach up to 64 meters. Draw a possible design for John. Solution Note that a regular octagon has 8 sides, and all of the sides have equal measures. Since John has 64 meters worth of fencing materials, each side of the octagon measures 8 meters. Let us construct a regular octagon with each side measuring 8 meters. Step 1: Draw a line. Step 2: At one end of the line, use a protractor to measure an angle of measure. Then, draw the next line at that angle. Step 3: Repeat Step 2 until the octagon is complete. 1.1. Constructing Regular and Irregular Polygons 13 Mathematics 7 Unit 1: Angles and Polygons Let’s Try It Maria wants to fence a playground in the shape of a regular hexagon. She has 60 meters worth of fencing materials. Draw a possible design for Maria. Check Your Understanding A. Write P on the line provided if the figure is a polygon and NP if it is not. __________ 1. __________ 2. __________ 3. __________ 4. __________ 5. 1.1. Constructing Regular and Irregular Polygons 14 Mathematics 7 Unit 1: Angles and Polygons B. Write R on the line provided if the polygon is regular and IR if it is irregular. __________ 1. __________ 2. __________ 3. __________ 4. __________ 5. C. Draw the following figures based on the given conditions. 1. Draw a square whose side measures 3 cm. 2. Draw a regular pentagon whose side measures 5 cm. 3. Draw a regular octagon whose side measures 4 cm. 4. Draw a rectangle with a length of 5 cm and a width of 3 cm. 5. Draw a triangle whose angles are 30°, 60°, and 90°. 1.1. Constructing Regular and Irregular Polygons 15 Mathematics 7 Unit 1: Angles and Polygons Key Points A polygon is a closed figure made up of line segments. ○ The side of a polygon refers to each of the line segments that enclose the polygon. ○ The vertex of a polygon refers to the point of intersection of the sides of a polygon. ○ The angle of a polygon refers to the opening that the two sides form. Regular polygons are polygons that have all sides of equal length and all angles of equal measure. Self-Assessment I think I need I have a basic I am confident Skills more time and understanding of that I can do this assistance. it. with ease. I can define regular and irregular polygons and determine the characteristics of polygons with 5, 6, 8, or 10 sides. I can utilize a ruler and a protractor to measure sides and angles accurately for constructing regular and irregular polygons. 1.1. Constructing Regular and Irregular Polygons 16 Mathematics 7 Unit 1: Angles and Polygons I think I need I have a basic I am confident Skills more time and understanding of that I can do this assistance. it. with ease. I can draw and describe triangles, quadrilaterals, and regular polygons (5, 6, 8, or 10 sides) with given angle measures. Re ection I find ______________________ the most interesting because ________________________________. I need to improve on ________________________ because ___________________________________. I need to practice _________________________ because ______________________________________. I plan to ___________________________________________________________________________________. 1.1. Constructing Regular and Irregular Polygons 17 Mathematics 7 Unit 1: Angles and Polygons Attributions Wooden tangram in seal or sea lion shape on wood background by bankrx is licensed under Envato License via Envato Elements. References Jurgensen, Ray C., Richard G. Brown, and John W. Jurgensen. 2000. Geometry. 5th ed. Boston: Houghton Mifflin. 1.1. Constructing Regular and Irregular Polygons 18  Math 7 Unit 1: Angles and Polygons Answer Key Warm-Up 1. What did you name your five-sided shape? Answer: “The five-sided shape is a pentagon.” 2. Were you able to make all sides and angles equal? What challenges did you encounter? Possible answer: “It was difficult to make all sides and angles equal since I had to plan the measurement of the sides and angles.” Let’s Try It 1. Determine if the following figure is a regular polygon or not. Solution: The figure is not a regular polygon since the sides do not have equal measures. Answer: The figure is not a regular polygon. 1.1. Constructing Regular and Irregular Polygons 19  Math 7 Unit 1: Angles and Polygons 2. Construct a regular hexagon. Solution: Step 1: Draw a line of any length. Step 2: Measure at one end of the line and draw another line at that angle. Make sure that the line has the same length as the previous line. Step 3: Repeat Step 2 until the hexagon is formed. Answer: 1.1. Constructing Regular and Irregular Polygons 20  Math 7 Unit 1: Angles and Polygons 3. Construct a quadrilateral with angles measuring , , , and. Solution: Step 1: Draw a line of any length. Step 2: Measure at one end of the line and draw another line at that angle. Do the same at the other end of the line. Step 3: Measure at one end of the side and connect it to the other side. The angle at the other end will have a measure of. Answer: 1.1. Constructing Regular and Irregular Polygons 21  Math 7 Unit 1: Angles and Polygons 4. Maria wants to fence a playground in the shape of a regular hexagon. She has 60 meters worth of fencing materials. Draw a possible design for Maria. Solution: A regular hexagon has 6 sides. Since Maria has 60 meters worth of fencing materials, then each side of the hexagon has 10 meters. Step 1: Draw a line. Step 2: Measure at one end of the line and draw another line at that angle. Make sure that the line has the same length as the previous line. Step 3: Repeat Step 2 until the hexagon is formed. Answer: 1.1. Constructing Regular and Irregular Polygons 22