1. POLYGONS

2. WARM UP!!!

3. polygon
not a polygon

4. What is a polygon? A polygon is a plane figure.
A polygon is a closed region.
A polygon is formed by three or more line segments as its sides.
Each side of a polygon intersects only one segment at each of its endpoints.
poli  “many angled”

5. Polygon or Not a Polygon?

6. Polygon or Not a Polygon?

7. Polygon or Not a Polygon?

8. Polygon or Not a Polygon?
Not Polygon
because sides are not line segments.

9. Polygon or Not a Polygon?

10. Polygon or Not a Polygon?
Not Polygon
because sides are intersecting at more than the endpoints.

11. Polygon or Not a Polygon?

12. Polygon or Not a Polygon?

13. Polygon or Not a Polygon?

14. Polygon or Not a Polygon?
Not Polygon
because sides are not intersecting at the endpoints.

15. Polygon or Not a Polygon?

16. Polygon or Not a Polygon?

17. Polygon or Not a Polygon?

18. Polygon or Not a Polygon?
Not Polygon
because sides are intersecting more than one other side at its endpoint.

19. Naming Polygons A B D C
Polygons are named by writing their consecutive vertices in order, such as ABCD or CDAB for the polygon above.
We cannot name the polygon as DBAC.

20. Polygons can be named by their number of sides.
Name of Polygon 3
triangle 4
quadrilateral 5
pentagon 6
hexagon 7
heptagon 8
octagon 9
nonagon 10
decagon 11
undecagon 12
dodecagon

21. Connecting to Prior Knowledge
Think of words beginning with the prefixes tri-, quad-, pent-, and oct-.
Examples: triathlon, quadriplegic, pentameter, and octopus.

22. Regions in a Polygon

23. Parts of a Polygon sides interior angles / vertex angles
consecutive sides
included angle
nonconsecutive sides
interior angles / vertex angles
consecutive angles
included side
nonconsecutive angles
exterior angles

24. Interior Angles of Polygons
In a triangle the sum of the interior angles =180o
In a quadrilateral the sum of the interior angles =360o
USING WHAT YOU KNOW ABOUT TRIANGLES PROVE IT!!

25. Interior Angles of Polygons
Now how about a pentagon?
In a pentagon the sum of the interior angles =540o

26. Interior Angles of Polygons
In any polygon, the sum of the interior angles is:
180 (sides – 2)
NOTE: sides-2 is equal to the number of triangles you can form in the interior of the polygon!
What is the sum of interior angles in a:
Hexagon – 720o
Octagon o
Decagon o

27. ALL POLYGONS???

28. ALL POLYGONS!

29. How can these polygons be divided into two groups?

30. Convex Polygons
Concave Polygons

31. Polygon Convexity
A polygonal region is convex if any segment joining any two points of the polygon is part of the interior region. If a polygon is not convex, then its is concave.

32. Convex or Concave?
Convex

33. Convex or Concave? Concave
because a segment connecting points on the polygon that will lie in the exterior can be drawn.

34. Convex or Concave?
Convex

35. Convex or Concave? Concave
A segment connecting points on the polygon will lie in the exterior.

36. Convex or Concave? Concave
A segment connecting points on the polygon will lie in the exterior.

37. Convex or Concave?
Convex

38. Convex or Concave? Concave
A segment connecting points on the polygon will lie in the exterior.

39. Concepts
EQUIANGULAR POLYGON
EQUILATERAL POLYGON
REGULAR POLYGON

40. ┌ ┌ ┌ ┌ ┌ ┌ ┌ ┌ EQUILATERAL but not EQUIANGULAR
EQUILATERAL and EQUIANGULAR ┌ ┌ ┌ ┌
EQUILATERAL and EQUIANGULAR
EQUIANGULAR but not EQUILATERAL ┌ ┌ ┌ ┌

41. Regular vs. Irregular polygons
Which of these is a regular pentagon?

42. Regular vs. Irregular polygons
Regular polygons are equilateral and equiangular
Examples???
Square, regular pentagon, equilateral triangle
Counterexamples???
Kite, rhombus, trapezoid, parallelogram, isosceles triangle

43. Parts of a Polygon Diagonals
A diagonal of a polygon is any segment that joins two nonconsecutive vertices. Figure shows five- sided polygon QRSTU. Segments QS , SU , UR , RT and QT are the diagonals in this polygon.

44. Practice
Exercise Set 6.1 on pages
#1-6, 9-12, 18, 19 B.
C. D.

45. polygon
not a polygon