Our Lesson

1. Our Lesson Polygons Confidential

2. In the given figure 1, AB || CD and AC || BD Find x Answer= 40° Find y Answer= 35° In the given figure 2, l || m Find x Answer= 135° Find y Answer= 135° Find z Answer= 45° Find w Answer= 45° Warm up Figure 1 Figure 2 Confidential

3. Lets recap what we have learned in the previous lesson • Parallel lines are two lines in a plane which do not meet even when produced indefinitely. • When a transversal cuts two parallel lines pairs, the sum of the interior angles on the same side of transversal is 180°. • When a transversal cuts two parallel lines pairs of corresponding angles are equal. • When a transversal cuts two parallel lines pairs of alternate interior angles are equal. Confidential

4. Two lines are parallel if any one of the following conditions hold: • Pairs of alternate interior angles are equal. • Pairs of corresponding angles are equal. • The sum of the interior angles on the same side of transversal is 180° Confidential

5. Let’s get started Polygon: A polygon is a closed plane figure with three or more sides that are all straight. The sides do not cross each other. Two sides meet at every vertex. Examples: • Triangle • Rectangle • Square • Pentagon • Hexagon Confidential

6. Types of Polygons • Concave polygon • Convex polygon • Regular polygon • Irregular polygon Confidential

7. Concave polygon If a polygon has a reflex angle (A reflex angle is greater than 180º and less than 360º) then it is said to be a concave polygon. Example: Confidential

8. Convex polygon A polygon that has all interior angles less than 180°. Every line segment between two vertices of the polygon does not go exterior to the polygon. Example: Regular pentagon Confidential

9. Regular polygon A regularpolygon's sides are all of the same length and its angles are the same size. Examples: Square Equilateral Triangle Regular hexagon Regular octagon Confidential

10. Irregular polygon If a polygon is not a regular polygon, then it is said to be an irregular polygon. Example: Quadrilateral Confidential

11. Names of Polygons Confidential

12. Quadrilateral Family Triangle Square Rectangle Parallelogram Pentagon Trapezium Confidential

13. Octagon Hexagon Heptagon Nonagon Decagon Confidential

14. Diagonals of a polygon A line segment connecting non-adjacent vertices of a polygon. Polygon has n (n-3) diagonals. 2 diagonal Confidential

15. Sum of Interior Angles of a Polygon Formula to find Sum of interior angles of a given polygon: Sum of Interior Angles= 180(n-2), n denotes the number of sides Note: Using the above formula, we can find the number of sides and the interior angles of a polygon. Confidential

16. Each Interior Angle of a Regular Polygon Let's state the general formula for finding each interior angle of a REGULAR polygon FORMULA:  Each interior angle of a regular polygon = 180(n-2) , where n represents number of sides. n Confidential

17. Exterior Angles of a Polygon An exterior angle of a polygon is formed by extending one side of the polygon. The sum of the exterior angles is ALWAYS equal to 360º. Formula: Each exterior angle (regular polygon) = 360 , where n represents number of sides. n Confidential

18. Examples • What is the name of the polygon with sides 9. Nonagon • How many diagonals in a decagon? 20 • Write the example of convex polygon. Regular pentagon • How do you find the number of sides from the formula sum of interior angles = 180(n-2) ? Solve for n • Find the sum of the exterior angles of nonagon? 360 Confidential

19. Your Turn • Name the polygon : Hexagon • Write the number of sides of a polygon: Octagon - 8 • Draw the diagram of the given polygon: Pentagon • Write polygon or not a polygon. Circle Not a polygon • Write the types of polygon. Concave, Convex, Regular and Irregular Confidential

20. Your Turn 6. The sum of the exterior angles is ALWAYS equal to _____. 360 degree 7. Find the sum of the exterior angles of a decagon. 360 degree 8. Find the measure of each exterior angle of a regular hexagon. 60 degree 9. Write the formula to find the sum of Interior angles of a polygon. 180(n-2) 10. Write the example of irregular polygon. Quadrilateral Confidential

21. Refreshment Time Confidential

22. Lets play a Game www.miniclip.com/games/monkey-lander/en/ Confidential

23. 1) Find the number of degrees in the sum of the interior angles of an Nonagon. Solution: An Nonagon has 9 sides.  So n = 9.  Using our formula from above, that gives us  180(9-2) = 180(7) = 1260. Confidential

24. 2) Each interior angle of a regular polygon measures 108.  How many sides does the polygon have ? First, set the formula (for each interior angle) equal to the number of degrees given. 180(n-2) / n = 108 Cross multiply, 108n = 180(n-2) Multiply 180 by (n-2), 108n = 180n – 360 Subtract 180n on both sides -72n = -360 Divide both sides by -72, n = 5 Confidential

25. 3) The measure of each exterior angle of a regular polygon is 45º.How many sides does the polygon have ? Set the formula equal to 45. 360/ n = 45 Cross multiply and solve for n. 360 = 45 n n = 8 Confidential

26. Lets review what we have learned in our lesson Polygons: A polygon is a closed plane figure made up of 3 or more line segments. Types of Polygons: Concave, Convex, Regular and Irregular. Names of Polygon according to the sides are Triangles, Quadrilateral, Pentagon, Hexagon, Heptagon, Octagon, Nonagon and Decagon. Confidential

27. Formulae Sum of Interior Angles= 180(n-2), n denotes the number of sides Each interior angle of a regular polygon = 180(n-2) where n represents number of sides. n Each exterior angle (regular polygon) = 360 , where n represents number of sides. n Confidential

28. You did great in your lesson today ! Do Practice the lesson surely Confidential