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.

polygons

1. POLY GON

2. Learning Competency: D raw 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.

3. Activity 1: Polygon Scavenger Hunt: Objective : Find examples of regular and irregular polygons in the classroom or at home. Materials : Ruler, protractor, worksheet with a table to record findings. Activity : Students will search for objects that resemble regular and irregular polygons and use a ruler and protractor to measure the sides and angles. They will record their findings, noting the number of sides, types of angles, and classifying each shape as regular or irregular.

4. Activity 2: Create Your Own Polygon: Objective : Construct polygons with given side lengths and angle measurements. Materials : Cardstock, ruler, protractor, scissors, glue. Activity : Students will receive a set of measurements for sides and angles. They will cut out strips of cardstock to match the side lengths, measure and mark the angles, and then assemble the polygons. Once completed, they will classify their polygons as regular or irregular.

5. Activity 3: Angle Investigation : Objective : Investigate the relationship between the number of sides and the sum of interior angles in polygons. Materials : Paper, pencil, protractor. Activity : Students will draw various regular and irregular polygons and measure each interior angle with a protractor. They will calculate the sum of the interior angles and verify if it matches the formula (n−2)×180∘ where ( n ) is the number of sides. They will record their findings and discuss the patterns observed.

6. ACTIVITY 4: Polygon Art: Objective : Create an artistic design using regular and irregular polygons. Materials : Colored paper, ruler, protractor, scissors, glue. Activity : Students will design a piece of art by drawing and cutting out regular and irregular polygons. They will arrange these shapes into a creative pattern or picture, overlapping and combining different polygons. The final artwork will display a variety of polygons, showcasing their understanding of the shapes’ properties.

7. WHAT IS POLYGON

8. A  polygon  is a two-dimensional geometric figure that consists of a finite number of straight line segments connected to form a closed shape. The segments are called sides or edges, and the points where two sides meet are known as vertices or corners. Polygons are named based on the number of sides they have; for example, a polygon with three sides is called a triangle, while one with four sides is known as a quadrilateral.

9. Polygon  comes from Greek.  Poly-  means "many" and  - gon  means "angle". Polygon  (straight sides ) Not a Polygon  (has a curve ) Not a Polygon  (open, not closed )

10. Here are some key characteristics of polygons: Closed Shape : The line segments connect in such a way that they form a closed loop, with no openings. Straight Sides : All sides of a polygon are straight, not curved. Vertices : The corners where the sides meet are called vertices. Interior Angles : The angles inside a polygon are called interior angles.

11. Types of Polygons Regular or Irregular A  regular  polygon has all angles equal and all sides equal, otherwise it is  irregular

12. REGULAR POLYGON

13. IRREGULAR POLYGON

14. When all angles are equal and all sides are equal it is regular, otherwise it is irregular

15. Concave or Convex A  convex  polygon has no angles pointing inwards. More precisely, no internal angle can be more than 180°. If any internal angle is greater than 180° then the polygon is  concave . ( Think: concave has a "cave" in it )

16. Simple or Complex A  simple  polygon has only one boundary, and it doesn't cross over itself. A  complex  polygon intersects itself! Many rules about polygons don't work when it is complex

17. Complex polygon

18. Names of Polygons     If it is a Regular Polygon... Name Sides Shape Interior Angle Triangle  (or Trigon) 3 60° Quadrilateral  (or Tetragon) 4 90° Pentagon 5 108° Hexagon 6 120° Heptagon (or Septagon) 7 128.571° Octagon 8 135°

19. Names of Polygons     If it is a Regular Polygon... Name Sides Shape Interior Angle Nonagon (or Enneagon) 9 140° Decagon 10 144° Hendecagon (or Undecagon) 11 147.273° Dodecagon 12 150° Triskaidecagon 13   152.308°  Tetrakaidecagon 14   154.286°  Pentadecagon 15   156° 

20. What is Concave, Complex? When any internal angle is greater than 180° (it points inwards) then it is  concave . ( Think: concave has a "cave" in it ), otherwise it is  convex . And a  complex  polygon intersects itself (the boundary crosses over), otherwise it is  simple  (like most polygons we deal with). Many rules about polygons don't work when they are complex.

21. When any internal angle is greater than 180° (it points inwards) then it is  concave . ( Think: concave has a "cave" in it ), otherwise it is  convex .

22. And a  complex  polygon intersects itself (the boundary crosses over), otherwise it is  simple  (like most polygons we deal with). Many rules about polygons don't work when they are complex.

23. EVALUATION

24. Question 1: Regular Pentagon Task : Draw a regular pentagon with each side measuring 4 cm. Questions : Measure and record the length of each side. Measure and record each interior angle. Calculate and record the sum of the interior angles. Is this polygon regular or irregular? Justify your answer.

25. Question 2: Irregular Hexagon Task : Draw an irregular hexagon with three sides measuring 3 cm and three sides measuring 4 cm. Questions : Measure and record the length of each side. Measure and record each interior angle. Calculate and record the sum of the interior angles. Is this polygon convex or concave? Justify your answer.

26. ASSESSMENT

27. What is a polygon? A. A 3-dimensional shape B. A shape made of straight lines and is closed C. A shape made of curves D. An open shape

28. What is a regular polygon? A. A polygon with all sides equal B. A polygon with all angles equal C. A polygon with all sides and angles equal D. A polygon with no sides equal

29. What is an irregular polygon? A. A polygon with all sides equal B. A polygon with all angles equal C. A polygon with all sides and angles equal D. A polygon with no sides and angles equal

30. What is a concave polygon? A. A polygon with no angles pointing inwards B. A polygon with at least one angle pointing inwards C. A polygon with all angles pointing inwards D. A polygon with no angles pointing outwards

31. What is a convex polygon? A. A polygon with no angles pointing inwards B. A polygon with at least one angle pointing inwards C. A polygon with all angles pointing inwards D. A polygon with no angles pointing outwards

32. What is a simple polygon? A. A polygon that intersects itself B. A polygon that does not intersect itself C. A polygon with all sides equal D. A polygon with all angles equal

33. What is a complex polygon? A. A polygon that intersects itself B. A polygon that does not intersect itself C. A polygon with all sides equal D. A polygon with all angles equal

34. How many sides does a hexagon have? A. 5 B. 6 C. 7 D. 8

35. How many sides does an octagon have? A. 5 B. 6 C. 7 D. 8

36. What is the interior angle of a regular pentagon? A. 60° B. 90° C. 108° D. 120°

37. ANSWER KEYS B C D B A B A B D C

38. Names of Polygons     If it is a Regular Polygon... Name Sides Shape Interior Angle Triangle  (or Trigon) 3 60° Quadrilateral  (or Tetragon) 4 90° Pentagon 5 108° Hexagon 6 120° Heptagon (or Septagon) 7 128.571° Octagon 8 135°

39. Names of Polygons     If it is a Regular Polygon... Name Sides Shape Interior Angle Nonagon (or Enneagon) 9 140° Decagon 10 144° Hendecagon (or Undecagon) 11 147.273° Dodecagon 12 150° Triskaidecagon 13   152.308°  Tetrakaidecagon 14   154.286°  Pentadecagon 15   156° 

40. THE SUM OF THE INTERIOR ANGLES