1. Find the polygon…
Click on the polygon.

2. Polygons are closed shapes. They cannot have openings.
Sorry…
Polygons are closed shapes.
They cannot have openings.

3. Polygons only have straight sides. They can’t have curves.
Sorry…
Polygons only have straight sides. They can’t have curves.

4. Polygons are closed shapes All triangles are polygons.
Congratulations!
Polygons are closed shapes
with straight sides.
All triangles are polygons.

5. Find the polygon…

6. Polygons only have straight sides.
Sorry…
Polygons only have straight sides.

7. Polygons only have straight sides.
Sorry…
Polygons only have straight sides.

8. All rectangles are polygons.
Excellent!
All rectangles are polygons.

9. Find the polygon…

10. Polygons are closed figures.
Sorry…
Polygons are closed figures.
They do not have holes.

11. Polygons’ sides do not cross each other
Sorry…
Polygons’ sides do not cross each other

12. All right!

13. (1-6) Angles of Polygons Poly means many and gon means angle.
The word ‘polygon’ is a Greek word.
Poly means many and gon means angle.

14. Definition of polygon A closed object
Made up of straight line segments
that do not cross each other
Vertex
Side

15. Names of some polygons Triangle Quadrilateral Pentagon Hexagon
Heptagon
Octagon
Nonagon
Decagon
n-gon
3-sides
4-sides
5-sides
6-sides
7-sides
8-sides
9-sides
10-sides
n -sides

16. What is the name of this polygon?
hexagon
octagon
pentagon a

17. How about this one? a
octagon
hexagon
pentagon

18. What is the name of this polygon?...
Quadrilateral
Pentagon
Triangle a

19. A polygon with six sides is called a hexagon.
True
False

20. A polygon with 5 vertices is called a quadrilateral.
True
False a

21. An octagon always has 8 equal sides.
True
False a

22. Congratulations!

23. Convex Polygons Concave Polygons
A polygon with no side points inwards when extended
Concave Polygons
A polygon with at least one side points inwards when extended.
(Think: concave has a "cave" in it)

24. Regular Polygons A polygon is regular when all the angles are equal
and all of the sides are congruent

25. Diagonals of Polygons Diagonal
A line segment that connects two non consecutive vertices of a polygon.

26. Interior angles of Polygons
4 sides
5 sides
2 x 180o = 360o
3 x 180o = 540o 2 3
180o
180o
180o
180o
180o
180o
6 sides
4 x 180o = 720o
7 sides 4
5 x 180o = 900o 5

27. Exterior angles of Polygons
An exterior angle of a regular polygon is formed by extending one side of the polygon.
Angle 1 is an exterior angle to angle 2 2 1
Exterior Angle + Interior Angle =180o

28. 1200
600
1200
600
600
1200

29. 1200
1200
1200

30. 1200

31. 3600

32. 600
600
600
600
600
600

33. 600
600
600
600
600
600

34. 1 2 3 4 5 6
600
600
600
600
600
600

35. 1 2 3 4 5 6
600

36. 3 4 2
3600 5 1 6

37. 900
900
900
900

38. 900
900
900
900

39. 900

40. 3 2
3600 4 1

41. Sum of exterior angles = 360º
Sum of Interior Angles = (n – 2) 180
# of sides
  Sum of exterior angles = 360º
exterior angle + interior angle = 180º
Regular polygons
Measure of each exterior angle of a regular polygon =
# of sides of a regular polygon =
# of sides

42. Example1: Find the measure of each interior angle of a regular nonagon
Step 1: Nonagon has 9 sides so n=9
Step 2: measure of each ext. angle =
Step 3: measure of interior angle =

43. Example2:
Find the measure of each exterior angle of a regular decagon.
Step 1: Decagon has 10 sides so n=10
Step 2: measure of each ext. angle =

44. Example3:
How many sides are there in a regular polygon if each interior angle
measures 165o?
Step 1: measure of exterior angle =
Step 2: # of sides of a regular polygon =

45. Example4:
Is it possible to have a regular polygon with an exterior angle equal to
40o ? If yes find the number of sides
Step 1: yes
Step 2: # of sides =

46. Homework
(12 – 30) even
pages 407, 408